Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C113 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14268661 |
| commutator, socle | C2×C113 | C2×C16 |
| Fitting | C4×C113 | C16 |
| hypercenter | C4 | #14268661 |
| hypocenter | C113 | M64 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ C4 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^40,g^b=g^112,g^c=g^18,g^d=g^98,g^e=g^11268 conjugacy classes — view the full character table.
| maximal subgroup of | #28407849, #28407850, #28407853, … |
| maximal normal subgroup of | #28407849, #28407850, #28407853, … |
| maximal quotient of | #28407843, #28407846, C4⋊#16813721, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1680);