Finite Group DatabasebetaFinite Group Databasebeta| order | 16170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C11⋊#64424) |
| unambiguous semidirect product | C11⋊(C5⋊#64424) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C11 | C2×C3 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 2695 |
A minimal faithful permutation representation — 3 generators on 30 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(13,14)(15,16)(18,21,22,19,20,23)(25,28,29,26,27,30);(1,2,4,6,8,10,11,9,7,5,3)(12,13,15,16,14)(24,25,27,30,29,28,26);(17,18,20,23,22,21,19)Polycyclic presentation:
2,3,5,7^2,11|c^a=c^4,d^a=d^6,e^a=e^6,f^a=f^10,d^b=d^2,e^b=e^2527 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C5⋊#64424, D55×#64424, D5×C11⋊#64424, … |
| maximal normal subgroup of | D11×C5⋊#64424, D55×#64424, D5×C11⋊#64424, … |
| maximal quotient of | C11⋊#15668734, C2×C5⋊(C11⋊#64424) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16170, 95);