Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C22×#14523982 |
| Fitting | C22×C16×C67 ⋊ C2 |
| Sylow | C67 ⋊ C22×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D67 |
| commutator | C2×C67 | C23×C8 |
| Frattini | C8 | C23×D67 |
| Fitting | C22×C16×C67 | C2 |
| socle | C23×C67 | C2×C8 |
| hypercenter | C22×C16 | D67 |
| hypocenter | C67 | C22×M32 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C8 ◁ C22×C16 | |
400 conjugacy classes of subgroups.
2192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30770669, #30770672, #30770702, … |
| maximal normal subgroup of | #30770669, #30770672, #30770702, … |
| maximal quotient of | C22×#16863171, C2×C4×#14523982, C22×(C2×D67)⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17605);