C₅₉×#13523 #28425632

order	15104
nilpotency class	4
isoclinism	isoclinic class of #13523
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#13523

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#2092
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₉
prime radical	C₂²×D₈×C₅₉	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₅₉×#405 ◁ G

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

normal subgroups only

This group has 308 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) = 1888

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

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

Conjugacy classes & character table

2006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6511);