C₁₀₃×#1917 #27191283

order	13184
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₃×#1917

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₀₃	C₂³
commutator	C₂³	C₂²×C₄×C₁₀₃
Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₃
socle, prime radical	C₂³×C₁₀₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₃ ◁ G

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 123
transitive degree	μ_t(G) = 13184

A minimal faithful permutation representation — 3 generators on 123 points:

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

Conjugacy classes & character table

4532 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₃×#1917, C₁₀₃×#21021, C₁₀₃×#21022, …
maximal normal subgroup of	C₂×C₁₀₃×#1917, C₁₀₃×#21021, C₁₀₃×#21022, …
maximal quotient of	C₁₀₃×#9537, C₁₀₃×#9538, C₁₀₃×#9539, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 649);

C103×#1917 #27191283