C₅₉×#8759 #28420868

order	15104
nilpotency class	3
isoclinism	isoclinic class of #8746
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#8759

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#381
commutator	C₂⁴	C₂²×C₄×C₅₉
Frattini, cosocle	C₂³×C₄	C₂³×C₅₉
prime radical	C₂⁵×C₅₉	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂³×C₄×C₅₉ ◁ G

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

normal subgroups only

This group has 474 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:

(1,2,5,12,7,11,3,13)(4,17,15,31,19,26,20,23)(6,10,21,24,14,22,16,8)(9,25,27,18,28,32,29,30)(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);(1,3,14,21)(2,8,22,12)(4,15,30,25)(5,6,16,7)(9,23,17,29)(10,13,11,24)(18,32,19,20)(26,27,28,31);(1,4)(2,9,10,26)(3,15)(5,20)(6,18)(7,19)(8,23,13,27)(11,28,22,17)(12,29,24,31)(14,30)(16,32)(21,25)

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, 1747);