C₁₀₁×AGL(1,ℤ/16) #27167535

order	12928
nilpotency class	4
isoclinism	isoclinic class of #2180
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₁×AGL(1,ℤ/16)

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₁	#442
commutator	C₈	C₂²×C₄×C₁₀₁
Frattini, cosocle	C₂×C₈	C₂³×C₁₀₁
prime radical	#509×C₁₀₁	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₁ ◁ C₂×C₄×C₁₀₁ ◁ #97×C₁₀₁ ◁ G

154 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 117
transitive degree	μ_t(G) = 1616

A minimal faithful permutation representation — 3 generators on 117 points:

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

Conjugacy classes & character table

2323 conjugacy classes. The character table is too large to display.

Relationships

maximal quotient of

C₁₀₁×#12065, C₁₀₁×#12067, C₁₀₁×#12077, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 913);