A₄×C₁₃×C₂₉ #17985334

order	4524
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₃×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	A₄×C₁₃×C₂₉
unambiguous semidirect product	C₂²⋊(C₃×C₁₃×C₂₉)
unambiguous semidirect product	(C₂²×C₂₉)⋊(C₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₁₃×C₂₉	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₁₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₂₉	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₁₃×C₂₉

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 1508

A minimal faithful permutation representation — 2 generators on 46 points:

(2,3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46);(1,2,3)

1508 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4524, 44);