C₅₉×#12440 #28424549

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12430
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#12440

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₅₉	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₅₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ C₈×Q₈×C₅₉ ◁ G

216 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 15104

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

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

Conjugacy classes & character table

2891 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5428);