C₅₉×#13416 #28425525

order	15104
nilpotency class	4
isoclinism	isoclinic class of #13373
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#13416

Subgroups

	subgroup	G/H
center	C₄×C₅₉	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₉
socle	C₂×C₅₉	#2041
prime radical	C₅₉×#3150	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×#97×C₅₉ ◁ G

442 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 91
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 3 generators on 91 points:

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

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, 6404);