CAYLEY   V3.8.3      (SUN4/UNIX)   Mon Sep  4 1995 20:13:38    STORAGE 200000


CAYLEY   V3.8.3      (SUN4/UNIX)   Mon Sep  4 1995 20:13:40    STORAGE 2000000

    Calculated Group - now starting on nonsparse elements
    Calculated nonsparse elements - now starting on subgroups
    Calculated subgroups - now starting on the final stretch home!!
     
    List of subgroups which would produce quotient polytopes
    (Actually, representatives of Conjugacy Classes of same)
    Also some additional information
    There are   10   subgroups listed.
     
     
    A[   1   ]   
GROUP IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S3 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S0 S1 S0
      S2 S3 S1 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S2 S0 S1 S0

    Normaliser: (Aut(A) is isomorphic to N/A)
    
GROUP OF ORDER 1440 = 2^5 * 3^2 * 5 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      (S3 S2 S1 S0)^5
      S2 S1 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S3 S2 S1 S0
      S0 S3
      S1 S3 S2 S3

    Core: (Gamma(A) is isomorphic to W/C)
    
GROUP OF ORDER 2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S0 S1 S0 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0
     S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3
     S2 S1 S0 S3 S2 S1 S3 S2 S3

     
     
    A[   2   ]   
GROUP IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S3 S2 S3 S1 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1
     S2 S0 S1 S0
     
 S1 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S1
     S2 S3 S1 S0

    Normaliser: (Aut(A) is isomorphic to N/A)
    
GROUP OF ORDER 1440 = 2^5 * 3^2 * 5 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1
     S3 S2 S1 S0
     
 S1 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S3 S2 S1 S3
     S2 S1 S0 S3
      S1 S0
      S0 S3 S2 S3
      S2 S1 S3 S2 S3 S2

    Core: (Gamma(A) is isomorphic to W/C)
    
GROUP OF ORDER 2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S0 S1 S0 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0
     S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3
     S2 S1 S0 S3 S2 S1 S3 S2 S3

     
     
    A[   3   ]   
GROUP IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S3 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S0 S1 S0
     
 S1 S2 S3 S2 S3 S1 S2 S3 S0 S1 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S1 S2 S3
     S1 S2 S1 S0

    Normaliser: (Aut(A) is isomorphic to N/A)
    
GROUP OF ORDER 720 = 2^4 * 3^2 * 5 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      (S3 S2 S1 S0)^5
     
 S1 S2 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S3 S2 S1 S3 S2
     S1 S0 S3 S2
      S0 S3 S2 S3
      S0 S1 S0 S3
      S1 S2 S3 S2 S1 S3 S2 S1

    Core: (Gamma(A) is isomorphic to W/C)
    
GROUP OF ORDER 2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S0 S1 S0 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0
     S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3
     S2 S1 S0 S3 S2 S1 S3 S2 S3

     
     
    A[   4   ]   
GROUP IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S3 S2 S3 S1 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1
     S2 S0 S1 S0

    Normaliser: (Aut(A) is isomorphic to N/A)
    
GROUP OF ORDER 480 = 2^5 * 3 * 5 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1
     S3 S2 S1 S0
      S0 S3 S2 S3
      S0 S1 S2 S1 S3 S2 S3 S2
      S1 S0 S3 S2 S1 S3

    Core: (Gamma(A) is isomorphic to W/C)
    
GROUP OF ORDER 2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S0 S1 S0 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0
     S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3
     S2 S1 S0 S3 S2 S1 S3 S2 S3

     
     
    A[   5   ]   
GROUP IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S3 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S0 S1 S0

    Normaliser: (Aut(A) is isomorphic to N/A)
    
GROUP OF ORDER 720 = 2^4 * 3^2 * 5 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      (S3 S2 S1 S0)^5
      S0 S3 S2 S3
      S0 S1 S0 S3
      S1 S2 S3 S2 S1 S3 S2 S1

    Core: (Gamma(A) is isomorphic to W/C)
    
GROUP OF ORDER 2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S0 S1 S0 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0
     S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3
     S2 S1 S0 S3 S2 S1 S3 S2 S3

     
     
    A[   6   ]   
GROUP IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S3 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3
     S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0
     S1 S2 S3 S0 S1 S2 S0 S1 S0

    A is Normal in W, hence polytope is strongly regular
    Normaliser: (Aut(A) is isomorphic to N/A)
    
GROUP OF ORDER 14400 = 2^6 * 3^2 * 5^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S0 S1 S0 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0
     S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3
     S2 S1 S0 S3 S2 S1 S3 S2 S3
      S0
      S1
      S2
      S3

    Core: (Gamma(A) is isomorphic to W/C)
    
GROUP OF ORDER 2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S0 S1 S0 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0
     S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3
     S2 S1 S0 S3 S2 S1 S3 S2 S3

     
     
    A[   7   ]   
GROUP IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S3 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3
     S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S0 S1 S0

    Normaliser: (Aut(A) is isomorphic to N/A)
    
GROUP OF ORDER 720 = 2^4 * 3^2 * 5 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      (S3 S2 S1 S0)^10
      S0 S3 S2 S3
      S0 S1 S0 S3
      S1 S2 S3 S2 S1 S3 S2 S1

    Core: (Gamma(A) is isomorphic to W/C)
    
GROUP OF ORDER 1 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      IDENTITY

     
     
    A[   8   ]   
GROUP IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S3 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S0 S1 S0

    Normaliser: (Aut(A) is isomorphic to N/A)
    
GROUP OF ORDER 1200 = 2^4 * 3 * 5^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      (S3 S2 S1 S0)^6
      S0 S3 S2 S3
      S1 S2 S3 S2

    Core: (Gamma(A) is isomorphic to W/C)
    
GROUP OF ORDER 1 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      IDENTITY

     
     
    A[   9   ]   
GROUP IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S3 S2 S3 S1 S2 S3 S1 S2 S3 S0 S1 S2 S3 S0 S1 S2 S3 S1 S2 S3 S0 S1 S2 S0 S1 S0

    Normaliser: (Aut(A) is isomorphic to N/A)
    
GROUP OF ORDER 200 = 2^3 * 5^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
     
 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1
      S1 S2 S3 S2
      S0 S1 S0 S2 S1 S0
      S3 S2 S1 S3 S2 S3
      S0 S1 S2 S3 S2 S1 S3 S2 S1 S0 S3 S2 S1 S0 S3 S2 S1 S3 S2 S3 S2 S1 S0

    Core: (Gamma(A) is isomorphic to W/C)
    
GROUP OF ORDER 1 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      IDENTITY

     
     
    A[   10   ]   
GROUP IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      IDENTITY

    A is Normal in W, hence polytope is strongly regular
    Normaliser: (Aut(A) is isomorphic to N/A)
    
GROUP OF ORDER 14400 = 2^6 * 3^2 * 5^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      IDENTITY
      S0
      S1
      S2
      S3

    Core: (Gamma(A) is isomorphic to W/C)
    
GROUP OF ORDER 1 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      IDENTITY


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