Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#16813619 |
| Fitting | C2×C42×C113 ⋊ C2 |
| Sylow | C113 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D113 |
| commutator | C22×C113 | C24 |
| Frattini | C22 | C23×D113 |
| Fitting | C2×C42×C113 | C2 |
| socle | C23×C113 | C23 |
| hypercenter | C2×C42 | D113 |
| hypocenter | C113 | C2×#127 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
498 conjugacy classes of subgroups.
1820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#20298341, #28389241, #28389243, … |
| maximal normal subgroup of | C2×#20298341, #28389241, #28389243, … |
| maximal quotient of | C2×#20298468, C2×#20298500, C4×#16813619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1089);