Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C23×C67⋊C16 |
| derived, Sylow | C67 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D67 |
| commutator, hypocenter | C67 | C23×C16 |
| Frattini | C8 | C23×D67 |
| Fitting | C23×C8×C67 | C2 |
| socle | C24×C67 | C8 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C23×C8 | |
440 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#22558286, C2×#22558287, #30770674, … |
| maximal normal subgroup of | C2×#22558286, C2×#22558287, #30770674, … |
| maximal quotient of | C22×C4×C67⋊C16, C22×C22⋊(C67⋊C16), C22×C4⋊(C67⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17603);