Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×(C13⋊C3)⋊D67 |
| unambiguous semidirect product | (C2×C13⋊C3)⋊(C3×D67) |
| Fitting, socle | C2×C3×C13×C67 ⋊ C2×C3 |
| derived, Hall | C13×C67 ⋊ C22×C32 |
| Hall | C3×C13⋊C3×C67 ⋊ C22 |
| Hall | C2×D871 ⋊ C32 |
| Hall | C3×C13⋊C3 ⋊ C2×D67 |
| Sylow | C67 ⋊ C2×C3×D13⋊C3 |
| Sylow | C13 ⋊ C2×C32×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | (C13⋊C3)⋊D67 |
| commutator, cosocle, hypocenter | C13×C67 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C13×C67 | C2×C3 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 ◁ C2×C3 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5226 |
1434 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 191);