C₅₉×#13580 #28425689

order	15104
nilpotency class	5
isoclinism	isoclinic class of #13578
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₅₉×#13580

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	C₂×#353
commutator	C₄²	C₂²×C₄×C₅₉
Frattini, cosocle	#124	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

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

normal subgroups only

This group has 402 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)(3,13,16,23)(4,9)(5,20)(6,11,22,27)(7,12)(8,15,24,32)(10,21,28,19)(14,29,31,25)(17,26,18,30)(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);(1,3,7,18)(2,8,12,25)(4,15,5,14)(6,16,22,17)(9,26,20,23)(10,13,28,30)(11,29,27,24)(19,32,21,31);(1,4,7,5)(2,9,12,20)(3,14,18,15)(6,19,22,21)(8,23,25,26)(10,27,28,11)(13,29,30,24)(16,31,17,32)

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, 6568);