C₁₀₉×#1917 #28359171

order	13952
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₉×#1917

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₀₉	C₂³
commutator	C₂³	C₂²×C₄×C₁₀₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₉
socle, prime radical	C₂³×C₁₀₉	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₉ ◁ G

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 129
transitive degree	μ_t(G) = 13952

A minimal faithful permutation representation — 3 generators on 129 points:

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

Conjugacy classes & character table

4796 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₉×#1917, C₁₀₉×#21021, C₁₀₉×#21022, …
maximal normal subgroup of	C₂×C₁₀₉×#1917, C₁₀₉×#21021, C₁₀₉×#21022, …
maximal quotient of	C₁₀₉×#9537, C₁₀₉×#9538, C₁₀₉×#9539, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 649);

C109×#1917 #28359171