C₁₀₁×#2053 #27167407

order	12928
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₁×#2053

Subgroups

	subgroup	G/H
center	C₄×C₁₀₁	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₁
socle	C₂×C₁₀₁	#394
prime radical	#575×C₁₀₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₁ ◁ C₂²×C₄×C₁₀₁ ◁ G

264 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

2626 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#12170, C₁₀₁×#12171, C₁₀₁×#12172, …
maximal normal subgroup of	C₁₀₁×#12170, C₁₀₁×#12171, C₁₀₁×#12172, …
maximal quotient of	C₁₀₁×#10464, C₁₀₁×#10465, C₁₀₁×#10466, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 785);