C₅₉×#13511 #28425620

order	15104
nilpotency class	4
isoclinism	isoclinic class of #13459
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#13511

Subgroups

	subgroup	G/H
center	C₄×C₅₉	#498
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₉
socle	C₂×C₅₉	#2084
prime radical	C₂³×C₅₉	#137
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×#97×C₅₉ ◁ G

250 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 110 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:

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

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, 6499);