Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C67 · Schur multiplier (H2) = C2 |
| direct product | D9×D13×C67 |
| unambiguous semidirect product | (C13×D9)⋊(C2×C67) |
| unambiguous semidirect product | (C9×D13)⋊(C2×C67) |
| unambiguous semidirect product | D117⋊(C2×C67) |
| Fitting, Hall | C9×C13×C67 ⋊ C22 |
| derived, Hall | C9×C13 ⋊ C22×C67 |
| Hall | C13×C67 ⋊ C2×D9 |
| Hall | C9×C67 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D9×C67 |
| Sylow | C9 ⋊ C2×D13×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | D9×D13 |
| commutator, cosocle, hypocenter | C9×C13 | C22×C67 |
| Frattini | C3 | D3×D13×C67 |
| Fitting | C9×C13×C67 | C22 |
| socle | C3×C13×C67 | C2×D3 |
| LCS | G ▷ C9×C13 | |
| UCS | C1 ◁ C67 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7839 |
3216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 57);