Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11744751 |
| derived, Sylow | C113 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D113 |
| commutator, hypocenter | C113 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D113 |
| Fitting | C2×C42×C113 | C2 |
| socle | C23×C113 | C2×C4 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C2×C42 | |
162 conjugacy classes of subgroups.
1856 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28388401, #28388408, #28388410, … |
| maximal normal subgroup of | #28388401, #28388408, #28388410, … |
| maximal quotient of | C2×C8×#11744751, C2×#20298319, M16×#11744751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 495);