Finite Group DatabasebetaFinite Group Databasebeta| order | 4032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×S42 |
| Fitting, socle | C24×C7 ⋊ D32 |
| derived | A42 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | S42 |
| commutator, cosocle, hypocenter | A42 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C24×C7 | D32 |
| LCS | G ▷ A42 | |
| UCS | C1 ◁ C7 | |
548 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×S42, D7×S42 |
| maximal normal subgroup of | ΓL(1,𝔽8)×S42, D7×S42 |
Past the SmallGroups library coverage — no SmallGroups id.