C₁₀₁×#1422 #27166776

order	12928
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₀₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₀₁×#1422

Subgroups

	subgroup	G/H
center	C₁₆×C₁₀₁	D₄
commutator	C₄	C₂×C₁₆×C₁₀₁
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₀₁
socle	C₂×C₁₀₁	C₄⋊C₁₆
prime radical	C₂²×C₁₀₁	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₁₀₁ ◁ C₂×C₁₆×C₁₀₁ ◁ G

58 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 133
transitive degree	μ_t(G) = 3232

A minimal faithful permutation representation — 2 generators on 133 points:

(1,2,5,11,6,9,19,22,7,10,20,24,3,13,14,26,8,12,21,25,15,23,28,31,4,17,18,30,16,27,29,32)(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);(1,3,4,6,8,16,7,15)(2,9,10,13,12,23,17,27)(5,14,18,19,21,29,20,28)(11,22,24,26,25,31,30,32)

Conjugacy classes & character table

5656 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#7381, C₁₀₁×#7382, C₁₀₁×#7447, …
maximal normal subgroup of	C₁₀₁×#7381, C₁₀₁×#7382, C₁₀₁×#7447, …
maximal quotient of	C₁₀₁×#7455, C₁₀₁×#7458, C₁₀₁×#7467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 154);

C101×#1422 #27166776