C₈×C₃₂×C₅₃ #27214840

order	13568
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₈

Aliases

abelian

C₈×C₃₂×C₅₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₁₆	C₂²×C₅₃
socle, prime radical	C₂²×C₅₃	C₄×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 93
transitive degree	μ_t(G) = 13568

A minimal faithful permutation representation — 2 generators on 93 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(33,34,35,36,37,38,39,40)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₈×C₅₃×C₆₄, C₁₆×C₃₂×C₅₃, C₂×C₈×C₃₂×C₅₃
maximal normal subgroup of	C₈×C₅₃×C₆₄, C₁₆×C₃₂×C₅₃, C₂×C₈×C₃₂×C₅₃
maximal quotient of	C₈×C₅₃×C₆₄, C₁₆×C₃₂×C₅₃, C₂×C₈×C₃₂×C₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 316);

C8×C32×C53 #27214840