C₅₉×#10523 #28422632

order	15104
nilpotency class	3
isoclinism	isoclinic class of #10518
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#10523

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
prime radical	C₂³×C₅₉	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

382 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 114 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:

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

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 3511);