C₅₉×#10130 #28422239

order	15104
nilpotency class	3
isoclinism	isoclinic class of #10128
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#10130

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
prime radical	C₅₉×#3205	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

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

normal subgroups only

This group has 520 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) = 3776

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

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

Conjugacy classes & character table

1829 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 3118);