Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | C2×D3×#1020⋊C2 |
| Fitting | C2×C3×#120 ⋊ C2×D3 |
| derived | C3×C22⋊A4 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×#1020⋊C2 |
| commutator, cosocle, hypocenter | C3×C22⋊A4 | C24 |
| Frattini | C22 | C22×D3×S4 |
| Fitting | C2×C3×#120 | C2×D3 |
| socle | C23×C3 | C22×S4 |
| LCS | G ▷ C3×C22⋊A4 | |
| UCS | C1 ◁ C2 | |
6062 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 6062 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
84 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.