Finite Group DatabasebetaFinite Group Databasebeta| order | 31702 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D1441 |
| unambiguous semidirect product | C11⋊(C11×D131) |
| unambiguous semidirect product | C131⋊(C11×D11) |
| Fitting, socle, Hall | C112×C131 ⋊ C2 |
| derived | C11×C131 ⋊ C2×C11 |
| Sylow | C131 ⋊ C11×D11 |
| Sylow | C112 ⋊ D131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D1441 |
| commutator, cosocle, hypocenter | C11×C131 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C131 | C2 |
| LCS | G ▷ C11×C131 | |
| UCS | C1 ◁ C11 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2882 |
7942 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31702, 8);