Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#11716106 |
| Fitting | C3×C4×C72 ⋊ C22 |
| Hall | C3×C72 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C2×D72 |
| commutator, cosocle | C2×C72 | C23×C3 |
| Frattini | C2 | C2×C3×D72 |
| Fitting | C3×C4×C72 | C22 |
| socle | C2×C3×C72 | C23 |
| hypercenter | C3×C4 | D72 |
| hypocenter | C72 | C2×C3×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 | |
264 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#11716106, C3×D4×D72, #72246546, … |
| maximal normal subgroup of | D3×#11716106, C3×D4×D72, #72246546, … |
Past the SmallGroups library coverage — no SmallGroups id.