Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C28 |
| direct product | C2×#95×D67 |
| Fitting | C2×#95×C67 ⋊ C2 |
| Sylow | C67 ⋊ C22×#95 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D67 |
| commutator | C2×C67 | C22×C42 |
| Frattini | C23 | C23×D67 |
| Fitting | C2×#95×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C2×#95 | D67 |
| hypocenter | C67 | C22×#95 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
1880 conjugacy classes of subgroups; only the 661 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 661 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 | #1280×D67, #30745429, #1294×D67, … |
| maximal normal subgroup of | #1280×D67, #30745429, #1294×D67, … |
| maximal quotient of | C4×#95×D67, C2×#95×Dic67, C22⋊#95×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 6833);