C₁₀₁×#2091 #27167445

order	12928
nilpotency class	3
isoclinism	isoclinic class of #2010
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₁×#2091

Subgroups

	subgroup	G/H
center	C₄×C₁₀₁	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₁
socle	C₂×C₁₀₁	#399
prime radical	C₂⁴×C₁₀₁	Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₁ ◁ C₂²×C₄×C₁₀₁ ◁ G

222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 117
transitive degree	μ_t(G) = 1616

A minimal faithful permutation representation — 3 generators on 117 points:

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

Conjugacy classes & character table

2626 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#7432, C₁₀₁×#7433, C₁₀₁×#12298, …
maximal normal subgroup of	C₁₀₁×#7432, C₁₀₁×#7433, C₁₀₁×#12298, …
maximal quotient of	C₁₀₁×#10659, C₁₀₁×#10660, C₁₀₁×#10661, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 823);

C101×#2091 #27167445