C₄₁×ΓL(1,𝔽₂₅) #14520127

order	1968
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₄₁ · Schur multiplier (H₂) = C₁

metacyclic
supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₄₁×ΓL(1,𝔽₂₅)

Splittings

Fitting	C₃×C₈×C₄₁ ⋊ C₂
Hall	C₃×C₄₁ ⋊ M₁₆
Sylow	C₃ ⋊ M₁₆×C₄₁

Subgroups

	subgroup	G/H
center	C₄×C₄₁	C₂×D₃
commutator	C₂×C₃	C₂×C₄×C₄₁
Frattini	C₄	C₂×D₃×C₄₁
Fitting	C₃×C₈×C₄₁	C₂
socle	C₂×C₃×C₄₁	C₂×C₄
prime radical	C₂×D₃×C₄₁	C₄
cosocle	C₃×C₄	C₂²×C₄₁
hypercenter	C₈×C₄₁	D₃
hypocenter	C₃	M₁₆×C₄₁
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₄₁ ◁ C₈×C₄₁

40 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)(45,46,47,50,48,49,51,52);(43,44)(46,49)(50,52)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 50);

C41×ΓL(1,𝔽25) #14520127