C₅₉×#13699 #28425808

order	15104
nilpotency class	5
isoclinism	isoclinic class of #13697
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#13699

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₅₉
prime radical	C₅₉×#2215	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂²×C₈×C₅₉ ◁ C₂²×C₁₆×C₅₉ ◁ G

200 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 74 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:

(1,2)(3,4)(6,11)(7,16)(8,17)(9,20)(12,19)(13,22)(14,30)(15,31)(18,27)(21,34)(23,24)(25,29)(26,35)(28,36)(32,33)(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);(5,6,12,26,8,14,18,25,20,29,33,30,34,35,7,11,10,13,16,24,21,28,32,31,9,15,27,36,17,23,19,22);(2,4)(6,13)(11,22)(14,28)(15,29)(23,35)(24,26)(25,31)(30,36)

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, 6687);