Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C113 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #11744762 |
| commutator, hypocenter | C113 | C64 |
| Fitting | C8×C113 | C8 |
| socle | C2×C113 | C32 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C8 | |
14 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^18,g^b=g^98,g^c=g^112176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20299680, #28407677, #28407678, … |
| maximal normal subgroup of | C2×#20299680, #28407677, #28407678, … |
| maximal quotient of | #28407572, C2×#20299680 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1631);