C₁₃₉×#10687 #48005283

order	35584
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃₉×#10687

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃₉	#124
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₉
socle	C₂²×C₁₃₉	#400
prime radical	C₂³×C₁₃₉	C₂²⋊Q₈
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ G

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

normal subgroups only

This group has 264 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) = 163
transitive degree	μ_t(G) = 8896

A minimal faithful permutation representation — 3 generators on 163 points:

(9,10,13,12,14,16,18,22)(11,17,19,24,20,21,23,15)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163);(1,2)(3,5)(4,7)(6,8)(9,11,18,19,14,20,13,23)(10,15,22,17,16,24,12,21);(2,5)(3,8)(6,7)(9,12,13,16,14,22,18,10)(11,17,19,24,20,21,23,15)

Conjugacy classes & character table

5560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35584, 3675);