Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#11761629 |
| Fitting | Q82×C67 ⋊ C2 |
| Sylow | C67 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D67 |
| commutator, socle | C22×C67 | C25 |
| Fitting | Q82×C67 | C2 |
| hypercenter | Q82 | D67 |
| hypocenter | C67 | Q8×#41 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
1068 conjugacy classes of subgroups; only the 529 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 529 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
875 conjugacy classes — view the full character table.
| maximal subgroup of | #30831806, #30831814, #30831821, … |
| maximal normal subgroup of | #30831806, #30831814, #30831821, … |
| maximal quotient of | C4⋊C4×#11761629, Q8×#14524001, #31015487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 18093);