C₅₉×#7313 #28419422

order	15104
nilpotency class	4
isoclinism	isoclinic class of #7313
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₅₉×#7313

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#1304
commutator	C₂²×C₄	C₄²×C₅₉
Frattini, cosocle	C₂²×#41	C₂²×C₅₉
prime radical	C₂²×#41×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂³×C₅₉ ◁ C₂²×#41×C₅₉ ◁ G

470 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 74 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 — 2 generators on 91 points:

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

Conjugacy classes & character table

1652 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 301);