C₁₃₉×#8630 #48003226

order	35584
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃₉×#8630

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃₉	#380
commutator	C₂²×C₄	C₂²×C₄×C₁₃₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₉
prime radical	#532×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂×C₄²×C₁₃₉ ◁ G

388 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 179
transitive degree	μ_t(G) = 17792

A minimal faithful permutation representation — 3 generators on 179 points:

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

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, 1618);