Finite Group DatabasebetaFinite Group Databasebeta| order | 31530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×(C1051⋊C3)⋊C5 |
| unambiguous semidirect product | (C2×C1051⋊C3)⋊C5 |
| unambiguous semidirect product | (C2×C1051⋊C5)⋊C3 |
| Fitting, socle, Hall | C2×C1051 ⋊ C3×C5 |
| derived, Sylow | C1051 ⋊ C2×C3×C5 |
| Hall | C2×C1051⋊C5 ⋊ C3 |
| Hall | C2×C1051⋊C3 ⋊ C5 |
| Hall | C1051⋊C5 ⋊ C2×C3 |
| Hall | C1051⋊C3 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C1051⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C1051 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1051 | C3×C5 |
| LCS | G ▷ C1051 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2102 |
170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31530, 4);