C₁₀₁×#2253 #27167607

order	12928
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₀₁×#2253

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

116 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:

(1,2,4,6)(3,7,8,5)(9,10,12,15)(11,19,21,33)(13,26,24,39)(14,27,25,18)(16,30,28,22)(17,32,29,20)(23,38,37,35)(31,36,34,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(1,3,4,8)(2,5,6,7)(10,15)(16,28)(17,29)(18,27)(19,33)(26,39)(31,34)(35,38);(9,11,20,36,14,23,24,30,12,21,32,40,25,37,13,22)(10,16,26,35,18,31,29,33,15,28,39,38,27,34,17,19)

Conjugacy classes & character table

3838 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#7452, C₁₀₁×#7454, C₁₀₁×#12463, …
maximal normal subgroup of	C₁₀₁×#7452, C₁₀₁×#7454, C₁₀₁×#12463, …
maximal quotient of	C₁₀₁×#12907, C₁₀₁×#13165, C₁₀₁×#13166, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 985);

C101×#2253 #27167607