Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×#11716029 |
| derived, Sylow | C72 ⋊ C2×C3×C8 |
| Hall | C3×C72 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | D72 |
| commutator, hypocenter | C72 | C2×C3×C8 |
| Frattini | C4 | C3×D72 |
| Fitting | C3×C4×C72 | C22 |
| socle | C2×C3×C72 | C2×C4 |
| prime radical | C2×C3×C7⋊D7 | C4 |
| cosocle | C4×C72 | C22×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C4 | |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#11716029, C3×#13096284, #72254209, … |
| maximal normal subgroup of | D3×#11716029, C3×#13096284, #72254209, … |
Past the SmallGroups library coverage — no SmallGroups id.