Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #123×Dic67 |
| Sylow | C67 ⋊ C4×#123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator | C22×C67 | C23×C4 |
| Fitting | C2×#123×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C2×#123 | D67 |
| hypocenter | C67 | C4×#123 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
688 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #352×Dic67, #30771797, #458×Dic67, … |
| maximal normal subgroup of | #352×Dic67, #30771797, #458×Dic67, … |
| maximal quotient of | #386×Dic67, #388×Dic67, #385×Dic67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 7033);