Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#16864146 |
| Sylow | C67 ⋊ C2×#563 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D67 |
| commutator | C22×C67 | C25 |
| Frattini | C22 | C24×D67 |
| Fitting | C2×#124×C67 | C2 |
| socle | C23×C67 | C24 |
| hypercenter | C2×#124 | D67 |
| hypocenter | C67 | C2×#563 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
1024 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
962 conjugacy classes — view the full character table.
| maximal subgroup of | #30748276, #30748279, #30771658, … |
| maximal normal subgroup of | #30748276, #30748279, #30771658, … |
| maximal quotient of | C2×#22563359, C2×#22563369, C2×#22563383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 18640);