Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #432×D67 |
| Fitting | #432×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#432 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D67 |
| commutator, socle | C22×C67 | C23×C4 |
| Fitting | #432×C67 | C2 |
| hypercenter | #432 | D67 |
| hypocenter | C67 | C2×#432 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ #432 | |
488 conjugacy classes of subgroups.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #1285×D67, #30745577, #30745581, … |
| maximal normal subgroup of | #1285×D67, #30745577, #30745581, … |
| maximal quotient of | #1745×D67, #1749×D67, #1767×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13127);