Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | 2−1+4×Dic67 |
| Sylow | C67 ⋊ C4×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D67 |
| commutator | C2×C67 | C24×C4 |
| Fitting | C2×2−1+4×C67 | C2 |
| socle | C22×C67 | C25 |
| hypercenter | C2×2−1+4 | D67 |
| hypocenter | C67 | C4×2−1+4 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
1492 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 1063 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30861722, #454×Dic67, #30861733, … |
| maximal normal subgroup of | #30861722, #454×Dic67, #30861733, … |
| maximal quotient of | #520×Dic67, #519×Dic67, #536×Dic67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 17723);