C₁₀₁×#1409 #27166763

order	12928
nilpotency class	5
isoclinism	isoclinic class of #1408
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₀₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₀₁×#1409

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₁	#353
commutator	C₄²	C₂×C₄×C₁₀₁
Frattini, cosocle	#127	C₂²×C₁₀₁
prime radical	#127×C₁₀₁	C₂²
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄×C₁₀₁ ◁ #127×C₁₀₁ ◁ G

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 117
transitive degree	μ_t(G) = 1616

A minimal faithful permutation representation — 2 generators on 117 points:

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

Conjugacy classes & character table

1717 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#7519, C₁₀₁×#7520, C₁₀₁×#7527, …
maximal normal subgroup of	C₁₀₁×#7519, C₁₀₁×#7520, C₁₀₁×#7527, …
maximal quotient of	C₁₀₁×#7355, C₁₀₁×#7371, C₁₀₁×#7403, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 141);

C101×#1409 #27166763