Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#14268648 |
| Fitting | C4×Q8×C113 ⋊ C2 |
| Sylow | C113 ⋊ C4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D113 |
| commutator | C2×C113 | C23×C4 |
| Frattini | C22 | C23×D113 |
| Fitting | C4×Q8×C113 | C2 |
| socle | C22×C113 | C24 |
| hypercenter | C4×Q8 | D113 |
| hypocenter | C113 | C4×#41 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
310 conjugacy classes of subgroups.
1160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28388955, #28388960, #28389007, … |
| maximal normal subgroup of | #28388955, #28388960, #28389007, … |
| maximal quotient of | C4×#16813580, C4×#16813584, C4×Q8×Dic113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1019);