Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×M32×D67 |
| Fitting | C2×M32×C67 ⋊ C2 |
| Sylow | C67 ⋊ C22×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D67 |
| commutator | C2×C67 | C23×C8 |
| Frattini | C8 | C23×D67 |
| Fitting | C2×M32×C67 | C2 |
| socle | C22×C67 | C22×C8 |
| hypercenter | C2×M32 | D67 |
| hypocenter | C67 | C22×M32 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C8 ◁ C2×M32 | |
400 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1375×D67, #30770679, #1376×D67, … |
| maximal normal subgroup of | #1375×D67, #30770679, #1376×D67, … |
| maximal quotient of | C2×#346×D67, C4×M32×D67, C2×M32×Dic67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17604);