C₁₁×A₄×C₂₃ #15690108

order	3036
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₁×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₁×A₄×C₂₃
unambiguous semidirect product	C₂²⋊(C₃×C₁₁×C₂₃)
unambiguous semidirect product	(C₂²×C₁₁)⋊(C₃×C₂₃)
unambiguous semidirect product	(C₂²×C₁₁×C₂₃)⋊C₃

	subgroup	G/H
center, hypercenter	C₁₁×C₂₃	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₁₁×C₂₃
Frattini	C₁	G
Fitting, socle	C₂²×C₁₁×C₂₃	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₁₁×C₂₃

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 1012

A minimal faithful permutation representation — 2 generators on 38 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38);(12,13,14)

1012 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3036, 27);