C₁₀₃×#1836 #27191202

order	13184
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₀₃×#1836

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

224 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₃×#7266, C₁₀₃×#7367, C₁₀₃×#8911, …
maximal normal subgroup of	C₁₀₃×#7266, C₁₀₃×#7367, C₁₀₃×#8911, …
maximal quotient of	C₁₀₃×#8786, C₁₀₃×#8789, C₁₀₃×#8794, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 568);