Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#16813672 |
| derived, Sylow | C113 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #90673 |
| commutator, hypocenter | C113 | C2×C32 |
| Frattini | C8 | C2×#90673 |
| Fitting | C2×C8×C113 | C4 |
| socle | C22×C113 | C16 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C2×C8 | |
34 conjugacy classes of subgroups.
512 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16813672, #28405679, #28405681, … |
| maximal normal subgroup of | C4×#16813672, #28405679, #28405681, … |
| maximal quotient of | C4×#16813672, C22⋊#16813672, C4⋊#16813672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1479);