Finite Group DatabasebetaFinite Group Databasebeta| order | 17130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×C571⋊C5 |
| unambiguous semidirect product | (C2×C3×C571)⋊C5 |
| Fitting, socle, Hall | C2×C3×C571 ⋊ C5 |
| derived, Sylow | C571 ⋊ C2×C3×C5 |
| Hall | C3×C571 ⋊ C2×C5 |
| Hall | C2×C571 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C571⋊C5 |
| commutator, cosocle, hypocenter | C571 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C571 | C5 |
| LCS | G ▷ C571 | |
| UCS | C1 ◁ C2×C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3426 |
714 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C4×C571⋊C5, C3×Dic571⋊C5, Dic3×C571⋊C5, … |
| maximal normal subgroup of | C3×C4×C571⋊C5, C3×Dic571⋊C5, Dic3×C571⋊C5, … |
| maximal quotient of | C3×C4×C571⋊C5, C22×C3×C571⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17130, 2);