C₄⁴×C₅₃ #27221256

order	13568
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄⁶

Aliases

abelian

C₄⁴×C₅₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂⁴	C₂⁴×C₅₃
socle, prime radical	C₂⁴×C₅₃	C₂⁴
LCS	G ▷ C₁
UCS	C₁ ◁ G

3966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 13568

A minimal faithful permutation representation — 4 generators on 69 points:

(1,2,3,4)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69);(5,6,7,8);(9,10,11,12);(13,14,15,16)

Conjugacy classes & character table

13568 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄³×C₈×C₅₃, C₂×C₄⁴×C₅₃
maximal normal subgroup of	C₄³×C₈×C₅₃, C₂×C₄⁴×C₅₃
maximal quotient of	C₄³×C₈×C₅₃, C₂×C₄⁴×C₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 6732);

C44×C53 #27221256