C₅₉×#10209 #28422318

order	15104
nilpotency class	3
isoclinism	isoclinic class of #10208
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#10209

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
prime radical	C₅₉×#3214	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

474 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 3776

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

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

Conjugacy classes & character table

1475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 3197);