C₅₉×#13678 #28425787

order	15104
nilpotency class	5
isoclinism	isoclinic class of #13677
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#13678

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#2196
commutator, Frattini, cosocle	#124	C₂³×C₅₉
LCS	G ▷ #124 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂²×C₅₉ ◁ C₂×C₄×C₅₉ ◁ #124×C₅₉ ◁ G

400 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 58 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:

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

Conjugacy classes & character table

1298 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6666);