C₁₀₃×#1845 #27191211

order	13184
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₀₃×#1845

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₀₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₀₃
Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 13184

A minimal faithful permutation representation — 3 generators on 119 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₃×#7269, C₁₀₃×#7274, C₁₀₃×#7370, …
maximal normal subgroup of	C₁₀₃×#7269, C₁₀₃×#7274, C₁₀₃×#7370, …
maximal quotient of	C₁₀₃×#8806, C₁₀₃×#8810, C₁₀₃×#8814, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 577);

C103×#1845 #27191211