C₅₉×#10611 #28422720

order	15104
nilpotency class	3
isoclinism	isoclinic class of #10611
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#10611

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
prime radical	C₂×#127×C₅₉	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

328 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 3776

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

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

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, 3599);