C₅₉×#13722 #28425831

order	15104
nilpotency class	5
isoclinism	isoclinic class of #13697
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₅₉×#13722

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₅₉
prime radical	C₂×D₁₆×C₅₉	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ C₄×C₈×C₅₉ ◁ C₄×C₁₆×C₅₉ ◁ G

184 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 99
transitive degree	μ_t(G) = 7552

A minimal faithful permutation representation — 3 generators on 99 points:

(1,2)(3,6)(4,5)(7,8)(9,10)(11,23)(12,19)(13,18)(14,34)(15,36)(16,22)(17,21)(20,28)(24,37)(25,31)(26,33)(27,32)(29,39)(30,38)(35,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(2,5)(6,8)(9,10,13,19,14,20,31,27,17,36,23,39,37,40,30,26,16,22,33,38,35,24,29,11,15,21,32,25,28,34,12,18);(1,3,4,7)(2,6,5,8)(9,11,12,24,28,38,32,22,15,26,29,40,35,39,33,36,16,27,30,20,37,19,23,10,17,18,31,34,14,25,13,21)

Conjugacy classes & character table

2714 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6710);