Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×D8×D67 |
| Fitting | C22×D8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C23×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D67 |
| commutator | C4×C67 | C25 |
| Frattini | C4 | C24×D67 |
| Fitting | C22×D8×C67 | C2 |
| socle | C23×C67 | C2×D4 |
| hypercenter | C22×D8 | D67 |
| hypocenter | C67 | C23×D8 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×D8 | |
1976 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1976 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
980 conjugacy classes — view the full character table.
| maximal subgroup of | #30771471, #30771492, #1879×D67, … |
| maximal normal subgroup of | #30771471, #30771492, #1879×D67, … |
| maximal quotient of | C22×#102×D67, C22×#107×D67, C2×C4×D8×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19224);