C₅₉×#13536 #28425645

order	15104
nilpotency class	4
isoclinism	isoclinic class of #13398
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#13536

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#481
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₉
prime radical	C₂³×C₅₉	C₂×SD₁₆
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×#97×C₅₉ ◁ G

318 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 95
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 3 generators on 95 points:

(5,6,12,29,24,34,8,15,11,16,26,13,10,17,9,25)(7,18,27,31,28,33,19,32,22,30,23,14,21,36,20,35)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(1,2)(3,4)(6,13,16,29)(8,12)(9,26)(10,24)(14,30,31,18)(15,17,25,34)(19,27)(20,23)(21,28)(32,36,35,33);(2,4)(5,7,11,22)(6,14,16,31)(8,23,9,27)(10,28,24,21)(12,20,26,19)(13,18,29,30)(15,33,25,36)(17,35,34,32)

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, 6524);