C₁₀₃×#1336 #27190702

order	13184
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₀₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₀₃×#1336

Subgroups

	subgroup	G/H
center	C₄×C₁₀₃	#102
commutator	C₈	C₂×C₈×C₁₀₃
Frattini, cosocle	C₄×C₈	C₂²×C₁₀₃
socle	C₂×C₁₀₃	D₄⋊C₈
prime radical	#135×C₁₀₃	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₃ ◁ C₂×C₈×C₁₀₃ ◁ C₄×C₈×C₁₀₃ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 1648

A minimal faithful permutation representation — 2 generators on 119 points:

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

Conjugacy classes & character table

3296 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₃×#1336, C₁₀₃×#11604, C₁₀₃×#11669, …
maximal normal subgroup of	C₂×C₁₀₃×#1336, C₁₀₃×#11604, C₁₀₃×#11669, …
maximal quotient of	C₁₀₃×#7070, C₁₀₃×#7071, C₁₀₃×#7072, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 68);

C103×#1336 #27190702