C₄₁×SL(2,ℤ/4) #14520177

order	1968
isoclinism	isoclinic class of S₄
automorphism	?
homology	Abelianization (H₁) = C₄×C₄₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₄₁×SL(2,ℤ/4)
unambiguous semidirect product	A₄⋊(C₄×C₄₁)

Splittings

derived

A₄ ⋊ C₄×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₁	S₄
commutator, hypocenter	A₄	C₄×C₄₁
Frattini	C₂	S₄×C₄₁
Fitting, socle	C₂³×C₄₁	D₃
prime radical	C₂×A₄×C₄₁	C₂
cosocle	C₂×A₄	C₂×C₄₁
LCS	G ▷ A₄
UCS	C₁ ◁ C₂×C₄₁

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 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)(42,43,44,45)(46,47,49,48);(47,48,49)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 100);

C41×SL(2,ℤ/4) #14520177