Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C28 |
| direct product | C22×D3×#120⋊C3 |
| Fitting | C22×C3×#120 ⋊ C2×C3 |
| derived | C24×C3 ⋊ C24×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×#120⋊C3 |
| commutator, cosocle, hypocenter | C24×C3 | C24×C3 |
| Frattini | C22 | C23×D3×A4 |
| Fitting | C22×C3×#120 | C2×C3 |
| socle | C24×C3 | C22×A4 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 ◁ C22 | |
15122 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 15122 conjugacy classes of subgroups — too many to draw. Only its 270 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#35346⋊C3, C22×D3×#1020⋊C2, C2×D3×#73081, … |
| maximal normal subgroup of | C22×D3×#1020⋊C2, C2×D3×#73081, C2×D3×AΣL(1,𝔽64) |
| maximal quotient of | C2×D3×AΣL(1,𝔽64), D3×#60399⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.