C₁₀₁×#3115 #27168469

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

Aliases

direct product

C₁₀₁×#3115

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 117
transitive degree	μ_t(G) = 6464

A minimal faithful permutation representation — 4 generators on 117 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₁×#9161, C₁₀₁×#9162, C₁₀₁×#9311, …
maximal normal subgroup of	C₁₀₁×#9161, C₁₀₁×#9162, C₁₀₁×#9311, …
maximal quotient of	C₁₀₁×#20743, C₁₀₁×#21122, C₁₀₁×#21124, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1847);

C101×#3115 #27168469