C₁₀₁×#2245 #27167599

order	12928
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₀₁×#2245

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₀₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₀₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₄²×C₁₀₁ ◁ C₄×C₈×C₁₀₁ ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 141
transitive degree	μ_t(G) = 12928

A minimal faithful permutation representation — 3 generators on 141 points:

(1,2)(3,5)(4,6)(7,8)(9,10,16,22)(11,18,26,37)(12,17,28,35)(13,20,30,32)(14,19,23,38)(15,31,29,21)(24,36,39,34)(25,40,27,33)(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);(1,3,4,7)(2,5,6,8)(9,11,23,39,15,25,13,12,16,26,14,24,29,27,30,28)(10,17,32,40,21,34,19,18,22,35,20,33,31,36,38,37);(2,6)(5,8)(9,12,13,27,29,39,23,26,16,28,30,25,15,24,14,11)(10,18,19,36,31,40,32,35,22,37,38,34,21,33,20,17)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₁×#12350, C₁₀₁×#12351, C₁₀₁×#12362, …
maximal normal subgroup of	C₁₀₁×#12350, C₁₀₁×#12351, C₁₀₁×#12362, …
maximal quotient of	C₁₀₁×#12890, C₁₀₁×#13150, C₁₀₁×#13207, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 977);

C101×#2245 #27167599