C₅₉×#12067 #28424176

order	15104
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#12067

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#442
commutator	C₈	C₂²×C₈×C₅₉
Frattini, cosocle	C₄×C₈	C₂³×C₅₉
prime radical	C₂×D₁₆×C₅₉	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ C₅₉×#322 ◁ G

246 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 83
transitive degree	μ_t(G) = 7552

A minimal faithful permutation representation — 3 generators on 83 points:

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

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, 5055);