Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×#72233459 |
| Fitting | C23×#120 ⋊ C3⋊D3 |
| derived | A4×C22⋊A4 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72233459 |
| commutator, cosocle, hypocenter | A4×C22⋊A4 | C23 |
| Frattini | C22 | C22×A4⋊S4 |
| Fitting | C23×#120 | C3⋊D3 |
| socle | C25 | C2×C3⋊S4 |
| LCS | G ▷ A4×C22⋊A4 | |
| UCS | C1 ◁ C2 | |
7192 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 7192 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72258621 |
| maximal normal subgroup of | C2×#72258621 |
Past the SmallGroups library coverage — no SmallGroups id.