Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×C4×D72 |
| Fitting | C3×C4×C72 ⋊ C22 |
| derived, Sylow | C72 ⋊ C22×C3×C4 |
| Hall | C3×C72 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | D72 |
| commutator, hypocenter | C72 | C22×C3×C4 |
| Frattini | C2 | C2×C3×D72 |
| Fitting | C3×C4×C72 | C22 |
| socle | C2×C3×C72 | C23 |
| prime radical | C2×C3×D72 | C2 |
| cosocle | C2×C72 | C23×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C4 | |
264 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D3×D72, C3×D4×D72, D72×D12, … |
| maximal normal subgroup of | C4×D3×D72, C3×D4×D72, D72×D12, … |
Past the SmallGroups library coverage — no SmallGroups id.