C₉×D₁₉ #66786

order	342
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₁₉

Fitting, Hall	C₉×C₁₉ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂×C₉

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 171

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2,4,3,5,7,6,8,9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28);(10,11,13,15,17,19,21,23,25,27,28,26,24,22,20,18,16,14,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(342, 4);