C₁₀₁×#2017 #27167371

order	12928
nilpotency class	3
isoclinism	isoclinic class of #2010
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₀₁×#2017

Subgroups

	subgroup	G/H
center	C₄×C₁₀₁	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₁
socle	C₂×C₁₀₁	#392
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₁ ◁ C₂²×C₄×C₁₀₁ ◁ G

350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 133
transitive degree	μ_t(G) = 3232

A minimal faithful permutation representation — 3 generators on 133 points:

(1,2)(3,12)(4,17)(5,22)(6,10)(7,11)(8,14)(9,20)(13,30)(15,25)(16,24)(18,29)(19,28)(21,27)(23,31)(26,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133);(1,3)(2,8)(4,18)(5,15)(6,14)(7,16)(9,26)(10,24)(11,25)(12,22)(13,19)(17,23)(20,31)(21,32)(27,30)(28,29);(1,4)(2,9)(3,13)(5,19)(6,20)(7,21)(8,23)(10,27)(11,28)(12,29)(14,18)(15,32)(16,31)(17,22)(24,26)(25,30)

Conjugacy classes & character table

2626 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#7406, C₁₀₁×#7407, C₁₀₁×#12117, …
maximal normal subgroup of	C₁₀₁×#7406, C₁₀₁×#7407, C₁₀₁×#12117, …
maximal quotient of	C₁₀₁×#9974, C₁₀₁×#9975, C₁₀₁×#9976, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 749);

C101×#2017 #27167371