Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28×C3 |
| direct product | C22×#10593630 |
| Fitting | C22×C3×#120 ⋊ D3 |
| derived | C3×C22⋊A4 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #10593630 |
| commutator, cosocle, hypocenter | C3×C22⋊A4 | C24 |
| Frattini | C22 | C23×C3⋊S4 |
| Fitting | C22×C3×#120 | D3 |
| socle | C24×C3 | C2×S4 |
| LCS | G ▷ C3×C22⋊A4 | |
| UCS | C1 ◁ C22 | |
6470 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 6470 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72231672, C22×D3×#1020⋊C2, C2×#72228416, … |
| maximal normal subgroup of | C22×D3×#1020⋊C2, C2×#72228416, C2×#72228412 |
| maximal quotient of | C2×#72228412, #72275114 |
Past the SmallGroups library coverage — no SmallGroups id.