C₃×C₄²×C₄₁ #14520158

order	1968
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7680
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian

C₃×C₄²×C₄₁

Subgroups

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

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 1968

A minimal faithful permutation representation — 2 generators on 52 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₄×C₈×C₄₁, C₂×C₃×C₄²×C₄₁, C₄²×C₉×C₄₁, …
maximal normal subgroup of	C₃×C₄×C₈×C₄₁, C₂×C₃×C₄²×C₄₁, C₄²×C₉×C₄₁, …
maximal quotient of	C₃×C₄×C₈×C₄₁, C₂×C₃×C₄²×C₄₁, C₄²×C₉×C₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 81);

C3×C42×C41 #14520158