C₁₀₁×#1839 #27167193

order	12928
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₀₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₁×#1839

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂³
commutator	C₂²	C₂²×C₈×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₁
socle, prime radical	C₂³×C₁₀₁	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₁ ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 125
transitive degree	μ_t(G) = 12928

A minimal faithful permutation representation — 3 generators on 125 points:

(1,2,3,5,4,6,7,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,23)(20,21)(22,24)(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);(9,11,12,15)(10,13,14,16)(18,21)(22,23);(10,14)(13,16)(17,19,20,24)(18,22,21,23)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₁×#7019, C₁₀₁×#7023, C₁₀₁×#7041, …
maximal normal subgroup of	C₁₀₁×#7019, C₁₀₁×#7023, C₁₀₁×#7041, …
maximal quotient of	C₁₀₁×#8800, C₁₀₁×#8801, C₁₀₁×#10795, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 571);

C101×#1839 #27167193