Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C113 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #11744762 |
| commutator, hypocenter | C113 | C2×C32 |
| Frattini | C4 | C2×#11744762 |
| Fitting | C8×C113 | C8 |
| socle | C2×C113 | C2×C16 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C8 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^18,g^b=g^112,g^c=g^98,g^d=g^112176 conjugacy classes — view the full character table.
| maximal subgroup of | #28407658, #28407661, C2×#20299705, … |
| maximal normal subgroup of | #28407658, #28407661, C2×#20299705, … |
| maximal quotient of | #28407657, #28407667, #28407673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1656);