CAYLEY   V3.8.3      (SUN4/UNIX)   Mon Sep  4 1995 20:05:07    STORAGE 200000


CAYLEY   V3.8.3      (SUN4/UNIX)   Mon Sep  4 1995 20:05:09    STORAGE 1000000

    Calculated Group - now starting on nonsparse elements
    Calculated nonsparse elements - now starting on subgroups
    Calculated subgroups - now checking for sparseness
     
    List of subgroups which would produce quotient polytopes
    Also some additional information
    There are   10   subgroups listed.
     
     
    A[   1   ]   
GROUP OF ORDER 1 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      IDENTITY

    A is Normal in W, hence M/A is strongly regular
    Normaliser: (Aut(M/A) is isomorphic to N/A)
    
GROUP OF ORDER 1152 = 2^7 * 3^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      IDENTITY
      S0
      S1
      S2
      S3

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

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

    A is Normal in W, hence M/A is strongly regular
    Normaliser: (Aut(M/A) is isomorphic to N/A)
    
GROUP OF ORDER 1152 = 2^7 * 3^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S0 S1 S0 S2 S1 S0 S2 S1 S2 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1 S0 S2 S1 S2 S3
      S0
      S1
      S2
      S3

    Core: (Gamma(M/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 S2 S1 S2 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1 S0 S2 S1 S2 S3

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

    Normaliser: (Aut(M/A) is isomorphic to N/A)
    
GROUP OF ORDER 144 = 2^4 * 3^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S1 S0 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1 S0 S2 S1 S2
      S0 S3
      S1 S3
      S1 S2 S1 S2 S3 S2

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

     
     
    A[   4   ]   
GROUP OF ORDER 3 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S1 S0 S2 S1 S0 S2 S1 S2 S3 S2 S1 S0 S2 S1 S2 S3

    Normaliser: (Aut(M/A) is isomorphic to N/A)
    
GROUP OF ORDER 144 = 2^4 * 3^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S1 S0 S2 S1 S0 S2 S1 S2 S3 S2 S1 S0 S2 S1 S2 S3
      S0 S3
      S1 S3
      S2 S1 S3 S2

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

     
     
    A[   5   ]   
GROUP OF ORDER 3 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S2 S1 S0 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1 S0 S2 S1

    Normaliser: (Aut(M/A) is isomorphic to N/A)
    
GROUP OF ORDER 144 = 2^4 * 3^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S2 S1 S0 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1 S0 S2 S1
      S0 S2 S1 S2
      S0 S2 S3 S2
      S0 S1 S0 S3

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

     
     
    A[   6   ]   
GROUP OF ORDER 3 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S1 S0 S2 S1 S0 S2 S1 S3 S2 S1 S0 S2 S1 S2 S3 S2

    Normaliser: (Aut(M/A) is isomorphic to N/A)
    
GROUP OF ORDER 144 = 2^4 * 3^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S1 S0 S2 S1 S0 S2 S1 S3 S2 S1 S0 S2 S1 S2 S3 S2
      S1 S3
      S0 S2 S1 S2

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

     
     
    A[   7   ]   
GROUP OF ORDER 3 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S0 S1 S2 S1 S0 S2 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1

    Normaliser: (Aut(M/A) is isomorphic to N/A)
    
GROUP OF ORDER 144 = 2^4 * 3^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S0 S1 S2 S1 S0 S2 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1
      S0 S2
      S0 S3
      S0 S1 S0 S2 S1 S2

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

     
     
    A[   8   ]   
GROUP OF ORDER 3 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S1 S2 S1 S0 S2 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1 S0

    Normaliser: (Aut(M/A) is isomorphic to N/A)
    
GROUP OF ORDER 144 = 2^4 * 3^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S1 S2 S1 S0 S2 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1 S0
      S0 S2
      S0 S3
      S1 S0 S2 S1

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

     
     
    A[   9   ]   
GROUP OF ORDER 3 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S2 S1 S0 S2 S1 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1 S0

    Normaliser: (Aut(M/A) is isomorphic to N/A)
    
GROUP OF ORDER 144 = 2^4 * 3^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S2 S1 S0 S2 S1 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1 S0
      S0 S2
      S0 S1 S0 S3
      S1 S3 S2 S1

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

     
     
    A[   10   ]   
GROUP OF ORDER 3 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S0 S2 S1 S0 S2 S1 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1

    Normaliser: (Aut(M/A) is isomorphic to N/A)
    
GROUP OF ORDER 144 = 2^4 * 3^2 IS A SUBGROUP OF W
GENERATORS AS WORDS IN SUPERGROUP :
      S0 S2 S1 S0 S2 S1 S3 S2 S1 S0 S2 S1 S2 S3 S2 S1
      S0 S2
      S1 S3
      S0 S1 S3 S2 S1 S2

    Core: (Gamma(M/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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