C₁₃₁×#11412 #45697296

order	33536
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₁₃₁ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₃₁×#11412

Subgroups

	subgroup	G/H
center	C₄×C₈×C₁₃₁	C₂³
commutator	C₂²	C₂×C₄×C₈×C₁₃₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₃₁
socle	C₂²×C₁₃₁	C₂×C₄×C₈
prime radical	C₂³×C₁₃₁	C₄×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₁₃₁ ◁ G

260 conjugacy classes of subgroups; only the 190 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 190 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) = 16768

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

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

Conjugacy classes & character table

14672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33536, 4400);