C₁₀₃×#3278 #27192644

order	13184
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₀₃×#3278

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₃
prime radical	#550×C₁₀₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₄×D₄×C₁₀₃ ◁ G

482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 123
transitive degree	μ_t(G) = 6592

A minimal faithful permutation representation — 4 generators on 123 points:

(1,2)(3,4)(5,6,10,8)(7,13,14,20)(9,17,19,12)(11,18,16,15)(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);(5,7,10,14)(6,11,8,16)(9,18,19,15)(12,20,17,13);(2,4)(7,14)(11,16)(13,20)(15,18);(5,8,10,6)(7,13,14,20)(9,12,19,17)(11,18,16,15)

Conjugacy classes & character table

2987 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₃×#19761, C₁₀₃×#19762, C₁₀₃×#19809, …
maximal normal subgroup of	C₁₀₃×#19761, C₁₀₃×#19762, C₁₀₃×#19809, …
maximal quotient of	C₁₀₃×#19889, C₁₀₃×#19897, C₁₀₃×#19907, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 2010);

C103×#3278 #27192644