C₁₀₃×#3183 #27192549

order	13184
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₀₃×#3183

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₃
prime radical	#469×C₁₀₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ G

370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 127
transitive degree	μ_t(G) = 6592

A minimal faithful permutation representation — 4 generators on 127 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₃×#11836, C₁₀₃×#33690
maximal normal subgroup of	C₁₀₃×#11836, C₁₀₃×#33690
maximal quotient of	C₁₀₃×#20825, C₁₀₃×#21286, C₁₀₃×#21287, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 1915);

C103×#3183 #27192549