C₅₉×#10303 #28422412

order	15104
nilpotency class	3
isoclinism	isoclinic class of #10300
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#10303

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
prime radical	C₂³×C₅₉	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

478 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 106 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:

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

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, 3291);