Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C8 |
| direct product | C82×D67 |
| Fitting | C82×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C82 | D67 |
| commutator, hypocenter | C67 | C2×C82 |
| Frattini | C42 | C22×D67 |
| Fitting | C82×C67 | C2 |
| socle | C22×C67 | C2×C42 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C82 | |
280 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×C16×D67, #1311×D67, C8×#14523982, … |
| maximal normal subgroup of | C8×C16×D67, #1311×D67, C8×#14523982, … |
| maximal quotient of | C82×Dic67, #1273×D67, #30746253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2782);