Finite Group DatabasebetaFinite Group Databasebeta| order | 17130 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D571⋊C3) |
| unambiguous semidirect product | (C571⋊C3)⋊D5 |
| unambiguous semidirect product | D2855⋊C3 |
| Fitting, socle, derived, Hall | C5×C571 ⋊ C2×C3 |
| Hall | C5×C571⋊C3 ⋊ C2 |
| Hall | D2855 ⋊ C3 |
| Hall | C571⋊C3 ⋊ D5 |
| Sylow | C571 ⋊ C3×D5 |
| Sylow | C5 ⋊ D571⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C571 | C2×C3 |
| LCS | G ▷ C5×C571 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2855 |
Polycyclic presentation:
2,3,5,571|c^a=c^4,d^a=d^570,d^b=d^109487 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D571⋊C3, C2×C5⋊(D571⋊C3) |
| maximal normal subgroup of | D5×D571⋊C3, C2×C5⋊(D571⋊C3) |
| maximal quotient of | (C571⋊C3)⋊Dic5, C2×C5⋊(D571⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17130, 17);