C₅₉×#7126 #28419235

order	15104
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₅₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₅₉×#7126

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#327
commutator	C₂×C₈	C₂×C₈×C₅₉
Frattini, cosocle	C₂×#97	C₂²×C₅₉
prime radical	C₂³×C₅₉	#102
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×#97×C₅₉ ◁ G

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

normal subgroups only

This group has 202 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) = 83
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 2 generators on 83 points:

(2,5,6,7)(9,10,12,17,13,19,11,20,14,18,21,15,23,24,22,16)(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);(1,2)(3,7)(4,6)(5,8)(10,15,18,17)(11,21)(12,22)(13,23)(16,19,20,24)

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 114);