Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22⋊Q8×Dic59 |
| Sylow | C59 ⋊ C4×C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C2×C22⋊Q8×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×C22⋊Q8 | D59 |
| hypocenter | C59 | C4×C22⋊Q8 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
656 conjugacy classes of subgroups.
868 conjugacy classes — view the full character table.
| maximal subgroup of | #328×Dic59, #28479580, #28479590, … |
| maximal normal subgroup of | #328×Dic59, #28479580, #28479590, … |
| maximal quotient of | #385×Dic59, #387×Dic59, #389×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7046);