C₅₉×#13658 #28425767

order	15104
nilpotency class	5
isoclinism	isoclinic class of #13657
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#13658

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#2177
commutator	C₁₆	C₂²×C₄×C₅₉
Frattini, cosocle	C₂×C₁₆	C₂³×C₅₉
prime radical	C₅₉×#2263	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₄×C₈×C₅₉ ◁ C₅₉×#346 ◁ G

194 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 82 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:

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

Conjugacy classes & character table

2006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6646);