C₁₃₁×#8783 #45694667

order	33536
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃₁×#8783

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃₁	#117
commutator	C₂²×C₄	C₂²×C₄×C₁₃₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₁
socle	C₂²×C₁₃₁	#382
prime radical	C₂³×C₁₃₁	#117
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ #376×C₁₃₁ ◁ G

262 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 8384

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

(1,2,5,8,4,7,12,15)(3,9,11,16,10,6,13,14)(17,18)(19,27,30,23)(20,31,33,46)(21,26)(22,25)(24,32,37,47)(28,41)(29,40,44,36)(34,38)(35,42)(39,48)(43,45)(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);(1,3)(2,6)(4,10)(5,11)(7,9)(8,14)(12,13)(15,16)(17,19,21,29,22,30,34,44)(18,23,26,36,25,27,38,40)(20,28,32,42,33,43,47,48)(24,35,31,45,37,39,46,41);(3,10)(6,9)(11,13)(14,16)(17,20)(18,24,25,37)(19,28)(21,32)(22,33)(23,35,27,39)(26,31,38,46)(29,42)(30,43)(34,47)(36,45,40,41)(44,48)

Conjugacy classes & character table

6812 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33536, 1771);