Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#16813712 |
| derived, Sylow | C113 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11744762 |
| commutator, hypocenter | C113 | C2×C32 |
| Frattini | C4 | C2×#11744762 |
| Fitting | C2×C4×C113 | C8 |
| socle | C22×C113 | C16 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C2×C4 | |
34 conjugacy classes of subgroups.
176 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16813712, #28407657, #28407659, … |
| maximal normal subgroup of | C4×#16813712, #28407657, #28407659, … |
| maximal quotient of | C4×#16813712, C22⋊#16813712, C4⋊#16813712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1655);