C₅₃×#10632 #27218144

order	13568
nilpotency class	3
isoclinism	isoclinic class of #10631
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₃×#10632

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₃	#397
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₃
prime radical	C₂³×C₅₃	#124
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

310 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 3392

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

(9,10,13,18,15,19,14,30)(11,20,22,32,24,36,23,16)(12,25,28,35,29,34,27,17)(21,31,26,40,38,39,37,33)(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);(1,2)(3,5)(4,7)(6,8)(9,11,15,24)(10,16,19,32)(12,26,29,37)(13,23,14,22)(17,33,35,40)(18,36,30,20)(21,27,38,28)(25,39,34,31);(2,5)(3,8)(6,7)(9,12,13,27,15,29,14,28)(10,17,18,34,19,35,30,25)(11,21,22,37,24,38,23,26)(16,31,20,33,32,39,36,40)

Conjugacy classes & character table

1802 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 3620);