Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C64×D67 |
| Fitting | C64×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C64 | D67 |
| commutator, hypocenter | C67 | C2×C64 |
| Frattini | C32 | C2×D67 |
| Fitting | C64×C67 | C2 |
| socle | C2×C67 | C2×C32 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C64 | |
40 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C128×D67, #30743741, C2×C64×D67, … |
| maximal normal subgroup of | C128×D67, #30743741, C2×C64×D67, … |
| maximal quotient of | C64×Dic67, (C2×D67)⋊C64, Dic67⋊C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2718);