C₄₁×#213 #14520137

order	1968
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₄₁×#213

Splittings

Fitting	C₃×D₄×C₄₁ ⋊ C₂
Hall	C₃×C₄₁ ⋊ D₈
Sylow	C₃ ⋊ D₈×C₄₁

Subgroups

	subgroup	G/H
center	C₂×C₄₁	#67
commutator, cosocle	C₃×C₄	C₂²×C₄₁
Frattini	C₄	C₂×D₃×C₄₁
Fitting	C₃×D₄×C₄₁	C₂
socle	C₂×C₃×C₄₁	D₄
hypercenter	D₄×C₄₁	D₃
hypocenter	C₃	D₈×C₄₁
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄₁ ◁ C₄×C₄₁ ◁ D₄×C₄₁

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 984

A minimal faithful permutation representation — 2 generators on 52 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)(46,49)(47,52)(50,51);(43,44)(45,46)(47,49)(48,51)(50,52)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 60);

C41×#213 #14520137