C₂²×C₁₁×C₁₃×C₂₅ #28384641

order	14300
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₁₁×C₁₃×C₂₅
multiplicative	(ℤ/21453)ˣ, (ℤ/28604)ˣ, (ℤ/42906)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₅×C₁₁×C₁₃
socle, prime radical	C₂²×C₅×C₁₁×C₁₃	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 14300

A minimal faithful permutation representation — 2 generators on 53 points:

(1,2)(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)(41,42,43,44,45,46,47,48,49,50,51,52,53);(3,4)

Conjugacy classes & character table

14300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₁₁×C₁₃×C₂₅, C₂³×C₁₁×C₁₃×C₂₅
maximal normal subgroup of	C₂×C₄×C₁₁×C₁₃×C₂₅, C₂³×C₁₁×C₁₃×C₂₅
maximal quotient of	C₂×C₄×C₁₁×C₁₃×C₂₅, C₂³×C₁₁×C₁₃×C₂₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14300, 13);

C22×C11×C13×C25 #28384641