C₅₉×#13519 #28425628

order	15104
nilpotency class	4
isoclinism	isoclinic class of #13309
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#13519

Subgroups

	subgroup	G/H
center	C₄×C₅₉	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₉
socle	C₂×C₅₉	#2087
prime radical	C₂³×C₅₉	#135
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×C₄×C₈×C₅₉ ◁ G

252 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 91
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 3 generators on 91 points:

(1,2,4,8,17,9,28,25,6,11,19,27,5,10,18,26)(3,12,15,21,20,29,32,22,14,30,31,23,13,24,16,7)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(3,13,14,20)(7,21,22,23)(12,29,30,24)(15,16,31,32);(1,3,5,20,6,14,17,13)(2,7,10,21,11,22,9,23)(4,16,18,15,19,32,28,31)(8,24,26,12,27,29,25,30)

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6507);