C₁₁×#3874⋊C₂ #15693158

order	3300
isoclinism	isoclinic class of #3874⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₁×#3874⋊C₂
unambiguous semidirect product	#3874⋊(C₂×C₁₁)
unambiguous semidirect product	((C₅⋊D₅)⋊C₃)⋊(C₂×C₁₁)

	subgroup	G/H
center, hypercenter	C₁₁	#3874⋊C₂
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁	C₂×D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₁₁

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 165

A minimal faithful permutation representation — 2 generators on 26 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 78);