C₁₀₃×#1422 #27190788

order	13184
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₀₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₀₃×#1422

Subgroups

	subgroup	G/H
center	C₁₆×C₁₀₃	D₄
commutator	C₄	C₂×C₁₆×C₁₀₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₀₃
socle	C₂×C₁₀₃	C₄⋊C₁₆
prime radical	C₂²×C₁₀₃	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₁₀₃ ◁ C₂×C₁₆×C₁₀₃ ◁ G

58 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 135
transitive degree	μ_t(G) = 3296

A minimal faithful permutation representation — 2 generators on 135 points:

(1,2,5,9,3,10,14,25,4,11,16,26,13,7,19,20,6,12,18,27,15,21,29,31,17,8,23,24,28,22,30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135);(1,3,4,13,6,15,17,28)(2,7,8,10,12,22,11,21)(5,14,16,19,18,29,23,30)(9,20,24,25,27,32,26,31)

Conjugacy classes & character table

5768 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₃×#7381, C₁₀₃×#7382, C₁₀₃×#7447, …
maximal normal subgroup of	C₁₀₃×#7381, C₁₀₃×#7382, C₁₀₃×#7447, …
maximal quotient of	C₁₀₃×#7455, C₁₀₃×#7458, C₁₀₃×#7467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 154);

C103×#1422 #27190788