Finite Group DatabasebetaFinite Group Databasebeta| order | 17130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D571⋊C3 |
| unambiguous semidirect product | (C5×D571)⋊C3 |
| Fitting, socle, Hall | C5×C571 ⋊ C2×C3 |
| derived, Sylow | C571 ⋊ C2×C3×C5 |
| Hall | C5×C571⋊C3 ⋊ C2 |
| Hall | C5×D571 ⋊ C3 |
| Hall | C571⋊C3 ⋊ C2×C5 |
| Hall | D571 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D571⋊C3 |
| commutator, cosocle, hypocenter | C571 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C571 | C2×C3 |
| LCS | G ▷ C571 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2855 |
505 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D571⋊C3, C2×C5×D571⋊C3 |
| maximal normal subgroup of | D5×D571⋊C3, C2×C5×D571⋊C3 |
| maximal quotient of | C5×(C571⋊C3)⋊C4, C2×C5×D571⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17130, 15);