Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q8×Dic226 |
| Sylow | C113 ⋊ Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D113 |
| commutator, socle | C22×C113 | C24 |
| Fitting | C4×Q8×C113 | C2 |
| hypercenter | C4×Q8 | D113 |
| hypocenter | C113 | Q82 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
212 conjugacy classes of subgroups.
1145 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28389651, #28389654, #28389713, … |
| maximal normal subgroup of | #28389651, #28389654, #28389713, … |
| maximal quotient of | Q8×#14268626, C4⋊C4×Dic226, Q8×C4⋊Dic113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1280);