Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×D9×D67 |
| unambiguous semidirect product | (D9×C67)⋊(C2×C13) |
| unambiguous semidirect product | (C9×D67)⋊(C2×C13) |
| unambiguous semidirect product | D603⋊(C2×C13) |
| Fitting, Hall | C9×C13×C67 ⋊ C22 |
| derived, Hall | C9×C67 ⋊ C22×C13 |
| Hall | C13×C67 ⋊ C2×D9 |
| Hall | C9×C13 ⋊ C2×D67 |
| Sylow | C67 ⋊ C2×C13×D9 |
| Sylow | C9 ⋊ C2×C13×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D9×D67 |
| commutator, cosocle, hypocenter | C9×C67 | C22×C13 |
| Frattini | C3 | D3×C13×D67 |
| Fitting | C9×C13×C67 | C22 |
| socle | C3×C13×C67 | C2×D3 |
| LCS | G ▷ C9×C67 | |
| UCS | C1 ◁ C13 | |
60 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, 53);