C₅₃×#13313 #27220825

order	13568
nilpotency class	4
isoclinism	isoclinic class of #13313
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₅₃×#13313

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₃	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₃
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂²×C₄×C₅₃ ◁ C₂×#131×C₅₃ ◁ G

556 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 89
transitive degree	μ_t(G) = 3392

A minimal faithful permutation representation — 3 generators on 89 points:

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

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, 6301);