Finite Group DatabasebetaFinite Group Databasebeta| order | 40320 |
| isoclinism | isoclinic class of A8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| direct product | C2×A8 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2 | A8 |
| commutator, hypocenter | A8 | C2 |
| Frattini | C1 | G |
| LCS | G ▷ A8 | |
| UCS | C1 ◁ C2 | |
473 conjugacy classes of subgroups; only the 4 normal subgroups are shown.
This group has 473 conjugacy classes of subgroups — too many to draw. Only its 4 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
28 conjugacy classes — view the full character table.
| automorphism group of | C24×C3 |
| outer automorphism group of | C24×C3 |
Past the SmallGroups library coverage — no SmallGroups id.