C₄₁×#216 #14520140

order	1968
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₄₁×#216

Splittings

Hall	C₃×C₄₁ ⋊ Q₁₆
Sylow	C₃ ⋊ Q₁₆×C₄₁

Subgroups

	subgroup	G/H
center	C₂×C₄₁	#67
commutator, cosocle	C₃×C₄	C₂²×C₄₁
Frattini	C₄	C₂×D₃×C₄₁
Fitting	C₃×Q₈×C₄₁	C₂
socle, prime radical	C₂×C₃×C₄₁	D₄
hypercenter	Q₈×C₄₁	D₃
hypocenter	C₃	Q₁₆×C₄₁
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄₁ ◁ C₄×C₄₁ ◁ Q₈×C₄₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 1968

A minimal faithful permutation representation — 2 generators on 60 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)(45,47,49,55)(46,50,52,59)(48,57,58,54)(51,60,56,53);(43,44)(45,46,49,52)(47,53,55,60)(48,56,58,51)(50,57,59,54)

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, 63);

C41×#216 #14520140