C₂×C₅₃×#1662 #27226497

order	13568
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₅₃×#1662

Subgroups

	subgroup	G/H
center, socle	C₂³×C₅₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₃
prime radical	C₂×C₅₃×#562	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

958 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 238 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) = 87
transitive degree	μ_t(G) = 6784

A minimal faithful permutation representation — 4 generators on 87 points:

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

Conjugacy classes & character table

2120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 11973);