C₁₀₁×#1658 #27167012

order	12928
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₁×#1658

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₀₁
prime radical	#127×C₁₀₁	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₄²×C₁₀₁ ◁ G

182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 133
transitive degree	μ_t(G) = 6464

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

(2,6)(4,11)(7,15)(8,12)(9,13)(14,16)(19,25)(20,27)(22,30)(23,28)(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);(1,2,5,8)(3,7,10,16)(4,12,11,6)(9,14,13,15)(17,18,21,24)(19,22,26,31)(20,28,27,23)(25,32,29,30);(1,3,5,10)(2,7,8,16)(4,13,11,9)(6,14,12,15)(17,19)(18,22)(20,29)(21,26)(23,32)(24,31)(25,27)(28,30)

Conjugacy classes & character table

2020 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#7524, C₂×C₁₀₁×#1658, C₁₀₁×#18990, …
maximal normal subgroup of	C₁₀₁×#7524, C₂×C₁₀₁×#1658, C₁₀₁×#18990, …
maximal quotient of	C₁₀₁×#7739, C₁₀₁×#7744, C₁₀₁×#7827, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 390);

C101×#1658 #27167012