C₅₉×#13692 #28425801

order	15104
nilpotency class	5
isoclinism	isoclinic class of #13691
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#13692

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#2206
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₅₉
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₄×C₈×C₅₉ ◁ C₄×C₁₆×C₅₉ ◁ G

216 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 70 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:

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

Conjugacy classes & character table

2183 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6680);