Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27×C3 |
| direct product | #41×A4⋊S4 |
| Fitting | C24×#41 ⋊ C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×A4⋊S4 |
| commutator, cosocle | C2×A42 | C24 |
| Frattini | C2 | C23×A4⋊S4 |
| Fitting | C24×#41 | C3⋊D3 |
| socle | C25 | C23×C3⋊D3 |
| hypercenter | #41 | A4⋊S4 |
| hypocenter | A42 | C2×#41 |
| LCS | G ▷ C2×A42 ▷ A42 | |
| UCS | C1 ◁ C4 ◁ #41 | |
14119 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 14119 conjugacy classes of subgroups — too many to draw. Only its 240 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
140 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.