C₅₉×#7524 #28419633

order	15104
nilpotency class	6
isoclinism	isoclinic class of #7523
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#7524

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#1404
commutator	#125	C₂×C₄×C₅₉
Frattini, cosocle	#490	C₂²×C₅₉
prime radical	#127×C₅₉	D₄
LCS	G ▷ #125 ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂²×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₄²×C₅₉ ◁ C₅₉×#490 ◁ G

134 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 30 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 — 2 generators on 91 points:

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

Conjugacy classes & character table

1121 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 512);