Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D169⋊C9) |
| unambiguous semidirect product | (C169⋊C9)⋊D5 |
| unambiguous semidirect product | D845⋊C9 |
| derived, Hall | C5×C169 ⋊ C2×C9 |
| Hall | C5×C169⋊C9 ⋊ C2 |
| Hall | D845 ⋊ C9 |
| Hall | C169⋊C9 ⋊ D5 |
| Sylow | C169 ⋊ C9×D5 |
| Sylow | C5 ⋊ D169⋊C9 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
Polycyclic presentation:
2,3,5,13,3,13|b^3=e,d^13=f^12,c^a=c^4,d^a=d^12f,f^a=f^12,d^b=d^3f^2,f^b=f^3456 conjugacy classes — view the full character table.
| maximal subgroup of | #16809981⋊C9, #16809980⋊C9, D5×D169⋊C9, … |
| maximal normal subgroup of | #16809981⋊C9, #16809980⋊C9, D5×D169⋊C9, … |
| maximal quotient of | Dic845⋊C9, C2×C5⋊(D169⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 4);