Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | D4×S42 |
| Fitting | C24×D4 ⋊ D32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×S42 |
| commutator, cosocle | C2×A42 | C24 |
| Fitting | C24×D4 | D32 |
| socle | C25 | C22×D32 |
| hypercenter | D4 | S42 |
| hypocenter | A42 | C22×D4 |
| LCS | G ▷ C2×A42 ▷ A42 | |
| UCS | C1 ◁ C2 ◁ D4 | |
18360 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 18360 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
125 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.