Finite Group DatabasebetaFinite Group Databasebeta| order | 2232 |
| isoclinism | isoclinic class of D31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×(C31⋊C3)⋊C4 |
| derived, Sylow | C31 ⋊ C2×C32×C4 |
| Hall | C3×C31⋊C3 ⋊ C2×C4 |
| Hall | C2×Dic31 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D31⋊C3 |
| commutator, hypocenter | C31 | C2×C32×C4 |
| Frattini | C2 | C2×C3×D31⋊C3 |
| Fitting, socle | C22×C3×C31 | C2×C3 |
| prime radical | C22×C3×C31⋊C3 | C2 |
| cosocle | C2×C31 | C22×C32 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C22×C3 | |
96 conjugacy classes of subgroups.
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×((C31⋊C3)⋊C4)⋊C5, C2×C3×C4×D31⋊C3, C2×D3×(C31⋊C3)⋊C4, … |
| maximal normal subgroup of | C2×C3×((C31⋊C3)⋊C4)⋊C5, C2×C3×C4×D31⋊C3, C2×D3×(C31⋊C3)⋊C4, … |
Past the SmallGroups library coverage — no SmallGroups id.