C₁₀₃×#2052 #27191418

order	13184
nilpotency class	3
isoclinism	isoclinic class of #2018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₃×#2052

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₃
prime radical	C₂×#41×C₁₀₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂²×C₄×C₁₀₃ ◁ G

262 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 6592

A minimal faithful permutation representation — 3 generators on 123 points:

(1,2)(3,4)(5,6)(7,15)(8,13)(9,12)(10,14)(11,17)(16,18)(19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(5,7,10,19)(6,11,14,16)(8,18,9,17)(12,20,13,15);(2,4)(5,6,8,12,10,14,9,13)(7,16,17,20,19,11,18,15)

Conjugacy classes & character table

2678 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₃×#2052, C₁₀₃×#23530, C₁₀₃×#23532, …
maximal normal subgroup of	C₂×C₁₀₃×#2052, C₁₀₃×#23530, C₁₀₃×#23532, …
maximal quotient of	C₁₀₃×#10458, C₁₀₃×#10459, C₁₀₃×#10462, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 784);