Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C4×C8×Dic67 |
| derived, Sylow | C67 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | D67 |
| commutator, hypocenter | C67 | C42×C8 |
| Frattini | C22×C4 | C22×D67 |
| Fitting | C2×C4×C8×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C4×C8 | |
408 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30742686, C82×Dic67, #322×Dic67, … |
| maximal normal subgroup of | #30742686, C82×Dic67, #322×Dic67, … |
| maximal quotient of | C82×Dic67, C4×C8×C67⋊C8, #322×Dic67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 4191);