C₁₀₁×#2298 #27167652

order	12928
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₀₁ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₀₁×#2298

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₀₁	C₂³
commutator	C₂²	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂³	C₂⁴×C₁₀₁
socle	C₂³×C₁₀₁	C₂⁴
prime radical	C₂⁴×C₁₀₁	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₁ ◁ G

524 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 121 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₁×#8732, C₁₀₁×#8733, C₁₀₁×#8740, …
maximal normal subgroup of	C₁₀₁×#8732, C₁₀₁×#8733, C₁₀₁×#8740, …
maximal quotient of	C₁₀₁×#13757, C₁₀₁×#13759, C₁₀₁×#13761, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1030);

C101×#2298 #27167652