Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | D67×C3⋊D39 |
| unambiguous semidirect product | (C3×D67)⋊D39 |
| unambiguous semidirect product | (C13×D67)⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C13×C67 ⋊ C22 |
| Hall | C13×C67 ⋊ C2×C3⋊D3 |
| Hall | C32×C67 ⋊ C2×D13 |
| Hall | C32×C13 ⋊ C2×D67 |
| Sylow | C67 ⋊ C2×C3⋊D39 |
| Sylow | C13 ⋊ C3⋊D3×D67 |
| Sylow | C32 ⋊ D13×D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C13×C67 | C22 |
| LCS | G ▷ C32×C13×C67 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7839 |
2100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 243);