Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C210 |
| direct product | C22×#87588⋊C2 |
| Fitting | C24×#120 ⋊ D3 |
| derived | C22⋊(C22⋊A4) ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #87588⋊C2 |
| commutator, cosocle, hypocenter | C22⋊(C22⋊A4) | C24 |
| Frattini | C22 | C23×#1020 |
| Fitting | C24×#120 | D3 |
| socle | C26 | C2×S4 |
| LCS | G ▷ C22⋊(C22⋊A4) | |
| UCS | C1 ◁ C22 | |
87447 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 87447 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
120 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.