C₁₀₃×#2189 #27191555

order	13184
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₃×#2189

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₀₃
prime radical	C₂×#135×C₁₀₃	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂²×C₄×C₁₀₃ ◁ C₂²×C₈×C₁₀₃ ◁ G

220 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 139
transitive degree	μ_t(G) = 6592

A minimal faithful permutation representation — 3 generators on 139 points:

(1,2)(3,4)(5,6,10,15)(7,16,20,34)(8,12,22,14)(9,23,25,29)(11,26,28,18)(13,30,32,21)(17,31,19,36)(24,33,35,27)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139);(5,7)(6,11)(8,17)(9,24)(10,20)(12,27)(13,31)(14,33)(15,28)(16,23)(18,21)(19,22)(25,35)(26,30)(29,34)(32,36);(2,4)(5,8,10,22)(6,12,15,14)(7,17,20,19)(9,21,25,30)(11,27,28,33)(13,29,32,23)(16,31,34,36)(18,35,26,24)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₀₃×#2189, C₁₀₃×#33516, C₁₀₃×#33519, …
maximal normal subgroup of	C₂×C₁₀₃×#2189, C₁₀₃×#33516, C₁₀₃×#33519, …
maximal quotient of	C₁₀₃×#12107, C₁₀₃×#12163, C₁₀₃×#12283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 921);