C₁₀₃×#1386 #27190752

order	13184
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₀₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₃×#1386

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	#102
commutator	C₈	C₄²×C₁₀₃
Frattini, cosocle	C₂²×C₈	C₂²×C₁₀₃
prime radical	C₂³×C₁₀₃	D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂²×C₄×C₁₀₃ ◁ C₂²×C₈×C₁₀₃ ◁ G

140 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 3296

A minimal faithful permutation representation — 2 generators on 123 points:

(1,2,3,4)(5,6)(7,11)(8,17)(9,13)(10,18)(12,16)(14,20)(15,19)(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);(5,7,9,17,10,18,20,16,11,6,12,14,19,15,8,13)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₀₃×#1386, C₁₀₃×#12567, C₄×#360×C₁₀₃, …
maximal normal subgroup of	C₂×C₁₀₃×#1386, C₁₀₃×#12567, C₄×#360×C₁₀₃, …
maximal quotient of	C₁₀₃×#7158, C₁₀₃×#7175, C₁₀₃×#7178, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 118);