C₄₁×C₂²⋊A₄ #14520276

order	1968
isoclinism	isoclinic class of C₂²⋊A₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₄₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product	C₄₁×C₂²⋊A₄
unambiguous semidirect product	C₂²⋊(A₄×C₄₁)
unambiguous semidirect product	(C₂²×C₄₁)⋊A₄

Splittings

Fitting, socle, Hall	C₂⁴×C₄₁ ⋊ C₃
derived, Sylow	C₂⁴ ⋊ C₃×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₄₁	C₂²⋊A₄
commutator, cosocle, hypocenter	C₂⁴	C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₂⁴×C₄₁	C₃
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₄₁

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 492

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)(43,44,45)(47,48,49);(46,49)(47,48);(42,45)(43,44)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 199);

C41×C22⋊A4 #14520276