C₁₀₃×#3233 #27192599

order	13184
nilpotency class	3
isoclinism	isoclinic class of #3186
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₀₃×#3233

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₃
prime radical	#121×C₁₀₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ G

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 135
transitive degree	μ_t(G) = 6592

A minimal faithful permutation representation — 4 generators on 135 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₃×#18659, C₁₀₃×#18661, C₁₀₃×#18671, …
maximal normal subgroup of	C₁₀₃×#18659, C₁₀₃×#18661, C₁₀₃×#18671, …
maximal quotient of	C₁₀₃×#21837, C₁₀₃×#21862, C₁₀₃×#21985, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 1965);

C103×#3233 #27192599