Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
| direct product | #95×Dic67 |
| Sylow | C67 ⋊ C4×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D67 |
| commutator | C2×C67 | C43 |
| Fitting | C2×#95×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C2×#95 | D67 |
| hypocenter | C67 | C4×#95 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
752 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 325 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 | #30746704, #327×Dic67, #30746709, … |
| maximal normal subgroup of | #30746704, #327×Dic67, #30746709, … |
| maximal quotient of | #30743750, #336×Dic67, #30760979, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 2729);