Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊Dic113 |
| Sylow | C113 ⋊ C22×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D113 |
| commutator | C2×C113 | C23×C4 |
| Frattini | C22 | C23×D113 |
| Fitting | C25×C113 | C2 |
| socle | C24×C113 | C22 |
| hypercenter | C25 | D113 |
| hypocenter | C113 | C22×C22⋊C4 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C24 ◁ C25 | |
674 conjugacy classes of subgroups.
1832 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28388796, #28388797, #28388811, … |
| maximal normal subgroup of | #28388796, #28388797, #28388811, … |
| maximal quotient of | C22×#16813529, C2×C4×C22⋊Dic113, C2×#20298454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 997);