C₁₀₁×#3269 #27168623

order	12928
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₀₁×#3269

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₄×D₄×C₁₀₁ ◁ G

478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 6464

A minimal faithful permutation representation — 4 generators on 121 points:

(1,2)(3,4)(5,6,11,14)(7,15,17,19)(8,13,10,9)(12,18,20,16)(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);(5,7,11,17)(6,12,14,20)(8,16,10,18)(9,15,13,19);(2,4)(5,8,11,10)(6,13,14,9)(7,16,17,18)(12,19,20,15);(5,9)(6,8)(7,12)(10,14)(11,13)(15,18)(16,19)(17,20)

Conjugacy classes & character table

2929 conjugacy classes. The character table is too large to display.

Relationships

maximal quotient of

C₁₀₁×#19760, C₁₀₁×#19768, C₁₀₁×#19778, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 2001);

C101×#3269 #27168623