C₁₁×D₁₉ #88272

order	418
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₁₉
unambiguous semidirect product	C₁₉⋊(C₂×C₁₁)

Fitting, socle, Hall	C₁₁×C₁₉ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂×C₁₁

	subgroup	G/H
center, hypercenter	C₁₁	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₁₁

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 209

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30);(12,13,15,17,19,21,23,25,27,29,30,28,26,24,22,20,18,16,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(418, 2);