#3055×C₁₃₁ #30663238

order	16768
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

#3055×C₁₃₁

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂³×C₄×C₁₃₁ ◁ G

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 143
transitive degree	μ_t(G) = 4192

A minimal faithful permutation representation — 4 generators on 143 points:

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

Conjugacy classes & character table

4192 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₃₁×#24412, C₁₃₁×#24414, C₁₃₁×#24416, …
maximal normal subgroup of	C₁₃₁×#24412, C₁₃₁×#24414, C₁₃₁×#24416, …
maximal quotient of	C₁₃₁×#19162, C₁₃₁×#19164, C₁₃₁×#19166, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16768, 1787);

#3055×C131 #30663238