C₃²×C₄×C₁₃×C₃₁ #28408191

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

Aliases

abelian

C₃²×C₄×C₁₃×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₃²×C₁₃×C₃₁
socle, prime radical	C₂×C₃²×C₁₃×C₃₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

72 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:

(1,2,3,4)(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);(8,9,10)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃²×C₈×C₁₃×C₃₁, C₂×C₃²×C₄×C₁₃×C₃₁
maximal normal subgroup of	C₃²×C₈×C₁₃×C₃₁, C₂×C₃²×C₄×C₁₃×C₃₁
maximal quotient of	C₃²×C₈×C₁₃×C₃₁, C₂×C₃²×C₄×C₁₃×C₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14508, 77);

C32×C4×C13×C31 #28408191