Finite Group DatabasebetaFinite Group Databasebeta| order | 17130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D571⋊C3)⋊C5 |
| unambiguous semidirect product | (D571⋊C5)⋊C3 |
| unambiguous semidirect product | ((C571⋊C3)⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C571 ⋊ C2×C3×C5 |
| Hall | (C571⋊C3)⋊C5 ⋊ C2 |
| Hall | D571⋊C5 ⋊ C3 |
| Hall | D571⋊C3 ⋊ C5 |
| Hall | C571⋊C5 ⋊ C2×C3 |
| Hall | C571⋊C3 ⋊ C2×C5 |
| Hall | D571 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C571 | C2×C3×C5 |
| LCS | G ▷ C571 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 571 |
Polycyclic presentation:
2,3,5,571|d^a=d^570,d^b=d^109,d^c=d^48149 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(D571⋊C3)⋊C5 |
| maximal normal subgroup of | C2×(D571⋊C3)⋊C5 |
| maximal quotient of | ((C571⋊C3)⋊C4)⋊C5, C2×(D571⋊C3)⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17130, 18);