C₅₉×#7809 #28419918

order	15104
nilpotency class	3
isoclinism	isoclinic class of #7734
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#7809

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₅₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

378 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 15104

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

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

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, 797);