C₅₃×#12897 #27220409

order	13568
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₅₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₃×#12897

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅₃	#117
commutator	C₂×C₄	C₂²×C₈×C₅₃
Frattini, cosocle	C₂²×C₈	C₂³×C₅₃
socle	C₂²×C₅₃	#432
prime radical	C₂³×C₅₃	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₂×#97×C₅₃ ◁ G

278 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 3392

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

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

Conjugacy classes & character table

3392 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 5885);