Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C113 ⋊ C2 |
| Sylow | C113 ⋊ #510 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^112,d^b=de,e^b=ef,g^b=g^1121136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28392464, #28392467, #28392526, … |
| maximal normal subgroup of | #28392464, #28392467, #28392526, … |
| maximal quotient of | #28392287, #28392295, #28392362, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 992);