C₁₀₁×#3009 #27168363

order	12928
nilpotency class	3
isoclinism	isoclinic class of #3008
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₀₁×#3009

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₁
prime radical	C₂×H(5,𝔽₂)×C₁₀₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×#41×C₁₀₁ ◁ G

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 3232

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

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

Conjugacy classes & character table

3232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#13097, C₁₀₁×#13100, C₁₀₁×#23894, …
maximal normal subgroup of	C₁₀₁×#13097, C₁₀₁×#13100, C₁₀₁×#23894, …
maximal quotient of	C₁₀₁×#18225, C₁₀₁×#18233, C₁₀₁×#18241, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1741);

C101×#3009 #27168363