Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C8×#11761629 |
| Fitting | C8×Q8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C8×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D67 |
| commutator | C2×C67 | C23×C8 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | C8×Q8×C67 | C2 |
| socle | C22×C67 | C23×C4 |
| hypercenter | C8×Q8 | D67 |
| hypocenter | C67 | C8×#41 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C8 ◁ C8×Q8 | |
456 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 225 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30765662, #30765672, #30765702, … |
| maximal normal subgroup of | #30765662, #30765672, #30765702, … |
| maximal quotient of | C8×#14524001, C8×#14524005, C8×Q8×Dic67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 13468);