Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16813690 |
| unambiguous semidirect product | D113⋊#106 |
| Fitting | C2×C8×C113 ⋊ C4 |
| Sylow | C113 ⋊ C2×#106 |
130 conjugacy classes of subgroups.
476 conjugacy classes — view the full character table.
| maximal subgroup of | #28405639, #28405640, #28405645, … |
| maximal normal subgroup of | #28405639, #28405640, #28405645, … |
| maximal quotient of | C2×#20299459, #28406116, C2×#20299460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1557);