C₅₃×#10646 #27218158

order	13568
nilpotency class	3
isoclinism	isoclinic class of #10645
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₃×#10646

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₃	#397
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₃
prime radical	C₂³×C₅₃	#126
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

236 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 101
transitive degree	μ_t(G) = 6784

A minimal faithful permutation representation — 3 generators on 101 points:

(1,2,4,9,6,10,5,8)(3,7,12,15,13,14,11,16)(17,18)(19,27,30,40)(20,24)(21,25)(22,26)(23,29,37,34)(28,43,31,42)(32,38)(33,39)(35,41)(36,45,47,44)(46,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,3)(2,7)(4,12)(5,11)(6,13)(8,16)(9,15)(10,14)(17,19,22,30)(18,23,26,37)(20,31,33,28)(21,34,35,29)(24,36,39,47)(25,40,41,27)(32,44,46,45)(38,43,48,42);(2,8)(3,11)(4,5)(7,14)(9,10)(12,13)(17,20,21,32,22,33,35,46)(18,24,25,38,26,39,41,48)(19,28,29,44,30,31,34,45)(23,36,27,42,37,47,40,43)

Conjugacy classes & character table

1643 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 3634);