C₅₃×#13720 #27221232

order	13568
nilpotency class	5
isoclinism	isoclinic class of #13694
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₅₃×#13720

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₅₃	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₅₃
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₄²×C₅₃ ◁ C₄×C₈×C₅₃ ◁ C₄×C₁₆×C₅₃ ◁ G

182 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 93 points:

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

Conjugacy classes & character table

3710 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 6708);