Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C67 · Schur multiplier (H2) = C23 |
| direct product | C2×#349×C67 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C22⋊C4 |
| commutator | C22 | C22×C8×C67 |
| Frattini, cosocle | C2×C8 | C23×C67 |
| socle | C22×C67 | C22⋊C8 |
| prime radical | C24×C67 | C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C22×C8×C67 ◁ G | |
236 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2948 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 846);