C₁₀₃×#1526 #27190892

order	13184
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₃×#1526

Subgroups

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

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 6592

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

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

Conjugacy classes & character table

3914 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₃×#8242, C₁₀₃×#8244, C₁₀₃×#8246, …
maximal normal subgroup of	C₁₀₃×#8242, C₁₀₃×#8244, C₁₀₃×#8246, …
maximal quotient of	C₁₀₃×#7564, C₁₀₃×#7570, C₁₀₃×#7632, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 258);

C103×#1526 #27190892