C₁₀₁×#3040 #27168394

order	12928
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₀₁×#3040

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₁
prime radical	C₂×AGL(1,ℤ/8)×C₁₀₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

500 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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₁×#9349, C₁₀₁×#9350, C₁₀₁×#24473, …
maximal normal subgroup of	C₁₀₁×#9349, C₁₀₁×#9350, C₁₀₁×#24473, …
maximal quotient of	C₁₀₁×#19274, C₁₀₁×#19275, C₁₀₁×#19276, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1772);

C101×#3040 #27168394