C₂×C₃×C₈×C₄₁ #14520161

order	1968
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1280
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian

C₂×C₃×C₈×C₄₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃×C₄₁
socle, prime radical	C₂²×C₃×C₄₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 1968

A minimal faithful permutation representation — 2 generators on 54 points:

(1,2,3,4,5,6,7,8)(11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54);(9,10)

Conjugacy classes & character table

1968 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₁₆×C₄₁, C₃×C₄×C₈×C₄₁, C₂²×C₃×C₈×C₄₁, …
maximal normal subgroup of	C₂×C₃×C₁₆×C₄₁, C₃×C₄×C₈×C₄₁, C₂²×C₃×C₈×C₄₁, …
maximal quotient of	C₂×C₃×C₁₆×C₄₁, C₃×C₄×C₈×C₄₁, C₂²×C₃×C₈×C₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 84);

C2×C3×C8×C41 #14520161