Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C67 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×C13⋊C3×C67 |
| unambiguous semidirect product | (C22×C13⋊C3)⋊(C3×C67) |
| unambiguous semidirect product | (A4×C13)⋊(C3×C67) |
| unambiguous semidirect product | (C22⋊(C13⋊C3))⋊(C3×C67) |
| Fitting, socle, Hall | C22×C13×C67 ⋊ C32 |
| derived, Hall | C22×C13 ⋊ C32×C67 |
| Hall | C13×C67 ⋊ C3×A4 |
| Hall | C22×C67 ⋊ C3×C13⋊C3 |
| Sylow | C13 ⋊ C3×A4×C67 |
| Sylow | C22 ⋊ C3×C13⋊C3×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | A4×C13⋊C3 |
| commutator, cosocle, hypocenter | C22×C13 | C32×C67 |
| Frattini | C1 | G |
| Fitting, socle | C22×C13×C67 | C32 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C67 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3484 |
1876 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 178);