Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2×C3 |
| direct product | C13×C3⋊D3×D67 |
| unambiguous semidirect product | (C3×D67)⋊(D3×C13) |
| Fitting, socle, Hall | C32×C13×C67 ⋊ C22 |
| derived, Hall | C32×C67 ⋊ C22×C13 |
| Hall | C13×C67 ⋊ C2×C3⋊D3 |
| Hall | C32×C13 ⋊ C2×D67 |
| Sylow | C67 ⋊ C2×C13×C3⋊D3 |
| Sylow | C32 ⋊ C2×C13×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C3⋊D3×D67 |
| commutator, cosocle, hypocenter | C32×C67 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C67 | C22 |
| LCS | G ▷ C32×C67 | |
| UCS | C1 ◁ C13 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7839 |
2730 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 240);