C₅₉×#12501 #28424610

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12483
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#12501

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₅₉
prime radical	C₂×D₈×C₅₉	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ C₈²×C₅₉ ◁ G

214 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 7552

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

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

Conjugacy classes & character table

2183 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5489);