Finite Group DatabasebetaFinite Group Databasebeta| order | 31174 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C1 |
| direct product | C11×C13×D109 |
| unambiguous semidirect product | C109⋊(C2×C11×C13) |
| Fitting, socle, Hall | C11×C13×C109 ⋊ C2 |
| derived, Sylow | C109 ⋊ C2×C11×C13 |
| Hall | C13×C109 ⋊ C2×C11 |
| Hall | C11×C109 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C13 | D109 |
| commutator, cosocle, hypocenter | C109 | C2×C11×C13 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C109 | C2 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C11×C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15587 |
8008 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31174, 2);