C₅₉×#13686 #28425795

order	15104
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#13686

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₅₉
prime radical	C₅₉×#2246	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ C₄×C₈×C₅₉ ◁ C₄×C₁₆×C₅₉ ◁ G

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

normal subgroups only

This group has 220 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) = 95
transitive degree	μ_t(G) = 7552

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

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

Conjugacy classes & character table

2891 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6674);