Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#16863153 |
| Sylow | C67 ⋊ C2×H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic67 |
| commutator | C4×C67 | C2×C42 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | C22×M16×C67 | C2 |
| socle | C22×C67 | #95 |
| hypercenter | C22×M16 | D67 |
| hypocenter | C67 | C2×H(3,ℤ/4) |
| LCS | G ▷ C4×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C4 ◁ C22×M16 | |
404 conjugacy classes of subgroups.
1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742962, #30742964, #30742968, … |
| maximal normal subgroup of | #30742962, #30742964, #30742968, … |
| maximal quotient of | C2×#22558037, #30745229, #30745232, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4211);