C₅₉×#13413 #28425522

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

Aliases

direct product

C₅₉×#13413

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#459
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₉
prime radical	C₂×C₅₉×#493	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×C₄×C₈×C₅₉ ◁ G

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

normal subgroups only

This group has 540 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) = 79
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 3 generators on 79 points:

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

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, 6401);