C₁₀₁×#1295 #27166649

order	12928
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₀₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₁×#1295

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₀₁	C₂²⋊C₄
commutator	C₂×C₄	C₄²×C₁₀₁
Frattini, cosocle	C₂×C₄²	C₂²×C₁₀₁
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 12928

A minimal faithful permutation representation — 2 generators on 121 points:

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

Conjugacy classes & character table

3838 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#7416, C₁₀₁×#7442, C₂×C₁₀₁×#1295, …
maximal normal subgroup of	C₁₀₁×#7416, C₁₀₁×#7442, C₂×C₁₀₁×#1295, …
maximal quotient of	C₁₀₁×#7025, C₁₀₁×#7030, C₁₀₁×#7036, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 27);

C101×#1295 #27166649