C₅₉×#13524 #28425633

order	15104
nilpotency class	4
isoclinism	isoclinic class of #13523
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#13524

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#2092
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₉
prime radical	C₂³×C₅₉	#135
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₅₉×#405 ◁ G

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

normal subgroups only

This group has 288 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) = 123
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 3 generators on 123 points:

(1,2,5,11,30,13,34,46,8,15,6,12,7,14,31,47)(3,16,18,50,19,48,32,38,21,52,57,37,20,44,28,9)(4,22,24,42,35,45,33,10,27,40,25,41,26,49,29,43)(17,36,53,58,23,59,60,64,55,62,61,63,54,39,56,51)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(1,3,7,19,8,21,30,20)(2,9,14,50,15,38,13,37)(4,23,26,55,27,54,35,17)(5,28,31,18,6,32,34,57)(10,39,42,36,43,59,41,62)(11,44,47,16,12,48,46,52)(22,58,49,64,40,63,45,51)(24,53,29,60,25,61,33,56);(1,4,8,27)(2,10,15,43)(3,17,21,55)(5,29,6,33)(7,35,30,26)(9,36,38,62)(11,45,12,49)(13,42,14,41)(16,51,52,64)(18,56,57,60)(19,54,20,23)(22,47,40,46)(24,34,25,31)(28,53,32,61)(37,59,50,39)(44,58,48,63)

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, 6512);