Finite Group DatabasebetaFinite Group Databasebeta| order | 15710 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D1571⋊C5 |
| unambiguous semidirect product | (C1571⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C1571 ⋊ C2×C5 |
| Hall | C1571⋊C5 ⋊ C2 |
| Hall | D1571 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1571 | C2×C5 |
| LCS | G ▷ C1571 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1571 |
Polycyclic presentation:
2,5,1571|c^a=c^1570,c^b=c^746167 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D1571⋊C5 |
| maximal normal subgroup of | C2×D1571⋊C5 |
| maximal quotient of | Dic1571⋊C5, C2×D1571⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15710, 1);