C₂²×C₃²×C₁₃×C₃₁ #28408239

order	14508
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian

C₂²×C₃²×C₁₃×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 14508

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

(1,2)(5,6,7)(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);(3,4)(8,9,10)

Conjugacy classes & character table

14508 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₄×C₁₃×C₃₁, C₂³×C₃²×C₁₃×C₃₁
maximal normal subgroup of	C₂×C₃²×C₄×C₁₃×C₃₁, C₂³×C₃²×C₁₃×C₃₁
maximal quotient of	C₂×C₃²×C₄×C₁₃×C₃₁, C₂³×C₃²×C₁₃×C₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14508, 125);

C22×C32×C13×C31 #28408239