C₁₀₁×#1400 #27166754

order	12928
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₀₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₀₁×#1400

Subgroups

	subgroup	G/H
center	C₈×C₁₀₁	C₂²⋊C₄
commutator	C₂²	C₂×C₁₆×C₁₀₁
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₀₁
socle	C₂×C₁₀₁	C₂²⋊C₁₆
prime radical	C₂³×C₁₀₁	C₁₆
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₀₁ ◁ C₂×C₁₆×C₁₀₁ ◁ G

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 133 points:

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

Conjugacy classes & character table

4444 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#7336, C₁₀₁×#7337, C₁₀₁×#7364, …
maximal normal subgroup of	C₁₀₁×#7336, C₁₀₁×#7337, C₁₀₁×#7364, …
maximal quotient of	C₁₀₁×#7334, C₁₀₁×#7362, C₁₀₁×#7380, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 132);

C101×#1400 #27166754