C₁₃₁×#13349 #45699233

order	33536
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃₁×#13349

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃₁	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂³×C₁₃₁
prime radical	C₂×H(5,𝔽₂)×C₁₃₁	C₂²
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂³×C₁₃₁ ◁ C₂²×D₄×C₁₃₁ ◁ G

780 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 151
transitive degree	μ_t(G) = 8384

A minimal faithful permutation representation — 3 generators on 151 points:

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

Conjugacy classes & character table

4061 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33536, 6337);