C₅₉×#13509 #28425618

order	15104
nilpotency class	4
isoclinism	isoclinic class of #13331
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#13509

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#459
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₉
prime radical	C₂³×C₅₉	AGL(1,ℤ/8)
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×C₄×C₈×C₅₉ ◁ G

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

normal subgroups only

This group has 268 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) = 99
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 3 generators on 99 points:

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

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, 6497);