C₅₉×#13447 #28425556

order	15104
nilpotency class	4
isoclinism	isoclinic class of #13312
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#13447

Subgroups

	subgroup	G/H
center	C₄×C₅₉	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₉
socle	C₂×C₅₉	#2054
prime radical	C₅₉×#3414	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₅₉×#405 ◁ G

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

normal subgroups only

This group has 386 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) = 123
transitive degree	μ_t(G) = 3776

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

(1,2)(3,16)(4,22)(5,29)(6,32)(7,12)(8,34)(9,15)(10,18)(11,25)(13,31)(14,30)(17,36)(19,46)(20,38)(21,45)(23,47)(24,55)(26,44)(27,58)(28,52)(33,40)(35,37)(39,51)(41,53)(42,56)(43,57)(48,60)(49,63)(50,62)(54,64)(59,61)(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)(2,10)(4,23)(5,19)(6,33)(7,18)(8,35)(9,21)(11,41)(12,37)(13,45)(14,46)(15,40)(16,29)(17,26)(20,30)(22,36)(24,49)(25,50)(27,48)(28,54)(31,51)(32,38)(34,39)(42,63)(43,64)(44,60)(47,55)(52,62)(53,56)(57,59)(58,61);(1,4,5,24,30,56,6,25,9,28,31,57,8,27,7,26)(2,11,12,42,34,55,13,22,15,44,32,58,14,43,29,52)(3,17,18,48,35,59,51,54,21,50,33,53,20,49,19,23)(10,36,16,47,46,63,38,41,40,62,45,64,39,61,37,60)

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, 6435);