C₁₀₁×#2248 #27167602

order	12928
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₀₁×#2248

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₀₁
prime radical	#493×C₁₀₁	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₄²×C₁₀₁ ◁ C₄×C₈×C₁₀₁ ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 6464

A minimal faithful permutation representation — 3 generators on 121 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₁×#12318, C₁₀₁×#12319, C₁₀₁×#12320, …
maximal normal subgroup of	C₁₀₁×#12318, C₁₀₁×#12319, C₁₀₁×#12320, …
maximal quotient of	C₁₀₁×#12505, C₁₀₁×#12509, C₁₀₁×#12510, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 980);

C101×#2248 #27167602