C₁₃₉×#7421 #48002017

order	35584
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃₉×#7421

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃₉	#357
commutator	C₂×C₁₆	C₂×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₃₉
prime radical	C₂³×C₁₃₉	SD₃₂
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂²×C₄×C₁₃₉ ◁ C₂²×C₈×C₁₃₉ ◁ C₂²×C₁₆×C₁₃₉ ◁ G

140 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 211
transitive degree	μ_t(G) = 17792

A minimal faithful permutation representation — 2 generators on 211 points:

(1,2)(3,7,8,5)(4,6)(9,10,13,19,16,23,39,22)(11,24,26,58,29,61,37,60)(12,30,33,67,36,53,72,68)(14,40,38,20,15,42,32,21)(17,44,45,25,49,62,48,64)(18,50,52,35,55,70,54,34)(27,65,41,59,28,66,43,51)(31,56,69,46,63,57,71,47)(73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211);(1,3)(2,5)(4,8)(6,7)(9,11,16,29)(10,17,23,49)(12,31,36,63)(13,37,39,26)(14,41,15,43)(18,51,55,59)(19,48,22,45)(20,56,21,57)(24,30,61,53)(25,34,64,35)(27,32,28,38)(33,71,72,69)(40,46,42,47)(44,50,62,70)(52,66,54,65)(58,68,60,67)

Conjugacy classes & character table

6811 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35584, 409);