C₅₉×#13586 #28425695

order	15104
nilpotency class	5
isoclinism	isoclinic class of #13584
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₅₉×#13586

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	C₂×#353
commutator	C₄²	C₂²×C₄×C₅₉
Frattini, cosocle	#127	C₂³×C₅₉
prime radical	C₅₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₅₉×#532 ◁ G

406 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 90 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)(3,12,14,7)(4,8)(5,10,20,9)(6,11)(13,28,29,21)(15,22,19,23)(16,30,31,24)(17,26,32,25)(18,27)(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);(1,3,6,15)(2,7,11,23)(4,16,18,13)(5,19,20,14)(8,24,27,21)(9,22,10,12)(17,29,32,31)(25,28,26,30);(1,4,6,18)(2,8,11,27)(3,13,15,16)(5,17,20,32)(7,21,23,24)(9,25,10,26)(12,28,22,30)(14,29,19,31)

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, 6574);