Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#11744762 |
| unambiguous semidirect product | (C2×#11744762)⋊C22 |
| Fitting | C23×C113 ⋊ C8 |
| Sylow | C113 ⋊ C2×C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#11744762 |
| commutator | C2×C113 | C22×C8 |
| Frattini | C2 | C22×#11744762 |
| Fitting | C23×C113 | C8 |
| socle | C22×C113 | C2×C8 |
| hypercenter | C23 | #11744762 |
| hypocenter | C113 | C2×C22⋊C8 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C23 | |
202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
152 conjugacy classes — view the full character table.
| maximal subgroup of | #28407583, #28407585, C2×#20299683, … |
| maximal normal subgroup of | #28407583, #28407585, C2×#20299683, … |
| maximal quotient of | C2×#20299683, C2×#20299684, #28407686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1660);