Finite Group DatabasebetaFinite Group Databasebeta| order | 31510 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C137 · Schur multiplier (H2) = C1 |
| direct product | C137×D115 |
| unambiguous semidirect product | C5⋊(D23×C137) |
| unambiguous semidirect product | C23⋊(D5×C137) |
| Fitting, socle, Hall | C5×C23×C137 ⋊ C2 |
| derived, Hall | C5×C23 ⋊ C2×C137 |
| Hall | C23×C137 ⋊ D5 |
| Hall | C5×C137 ⋊ D23 |
| Sylow | C23 ⋊ D5×C137 |
| Sylow | C5 ⋊ D23×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C137 | D115 |
| commutator, cosocle, hypocenter | C5×C23 | C2×C137 |
| Frattini | C1 | G |
| Fitting, socle | C5×C23×C137 | C2 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C137 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15755 |
8083 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31510, 7);