C₁₀₁×#2183 #27167537

order	12928
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₀₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₀₁×#2183

Subgroups

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

126 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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₁×#7393, C₁₀₁×#12049, C₁₀₁×#12051, …
maximal normal subgroup of	C₁₀₁×#7393, C₁₀₁×#12049, C₁₀₁×#12051, …
maximal quotient of	C₁₀₁×#12662, C₁₀₁×#12663, C₁₀₁×#13104, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 915);

C101×#2183 #27167537