C₂×C₁₁×D₁₁ #92152

order	484
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₁×D₁₁
unambiguous semidirect product	C₁₁⋊(C₂²×C₁₁)
unambiguous semidirect product	(C₂×C₁₁)⋊(C₂×C₁₁)

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₁²	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₁

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 44

A minimal faithful permutation representation — 2 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(484, 10);