C₂×C₅₃×#1840 #27228283

order	13568
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₅₃×#1840

Subgroups

	subgroup	G/H
center	C₂³×C₄×C₅₃	C₂³
commutator	C₂³	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
socle, prime radical	C₂⁴×C₅₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₅₃ ◁ G

894 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 462 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) = 13568

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)(58,60)(59,61)(62,63)(64,65)(66,70)(67,68)(69,71)(72,73,75,78,76,79,82,85)(74,77,81,84,80,83,86,87);(56,58,59,62)(57,60,61,63)(65,68)(69,70)(72,74)(73,77)(75,81)(76,80)(78,84)(79,83)(82,86)(85,87);(57,61)(60,63)(64,66,67,71)(65,69,68,70)(74,80)(77,83)(81,86)(84,87)

Conjugacy classes & character table

4664 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 13759);