Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C26×C3 |
| direct product | A42×#120 |
| Fitting, Sylow | C24×#120 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×A42 |
| commutator, socle, cosocle | C26 | C23×C32 |
| Fitting | C24×#120 | C32 |
| hypercenter | #120 | A42 |
| hypocenter | C24 | C32×#120 |
| LCS | G ▷ C26 ▷ C24 | |
| UCS | C1 ◁ C22 ◁ #120 | |
37820 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 37820 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
224 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.