Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C8×C113 ⋊ C4 |
| Sylow | C113 ⋊ #340 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,c^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^98,g^d=g^112476 conjugacy classes — view the full character table.
| maximal subgroup of | #28405560, #28405561, #28405562, … |
| maximal normal subgroup of | #28405560, #28405561, #28405562, … |
| maximal quotient of | #28405404, #28405409, #28405428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1423);