C₅₃×#12167 #27219679

order	13568
nilpotency class	4
isoclinism	isoclinic class of #12108
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₃×#12167

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₃	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₃
prime radical	C₅₃×#3259	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂²×C₄×C₅₃ ◁ C₅₃×#424 ◁ G

354 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 6784

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

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

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, 5155);