Finite Group DatabasebetaFinite Group Databasebeta| order | 31178 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C131 · Schur multiplier (H2) = C1 |
| direct product | C131×D119 |
| unambiguous semidirect product | C7⋊(D17×C131) |
| unambiguous semidirect product | C17⋊(D7×C131) |
| Fitting, socle, Hall | C7×C17×C131 ⋊ C2 |
| derived, Hall | C7×C17 ⋊ C2×C131 |
| Hall | C17×C131 ⋊ D7 |
| Hall | C7×C131 ⋊ D17 |
| Sylow | C17 ⋊ D7×C131 |
| Sylow | C7 ⋊ D17×C131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C131 | D119 |
| commutator, cosocle, hypocenter | C7×C17 | C2×C131 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C131 | C2 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C131 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15589 |
7991 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31178, 7);