C₁₀₉×#1710 #28358964

order	13952
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₀₉×#1710

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₀₉	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₁₀₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₉ ◁ C₄²×C₁₀₉ ◁ G

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 141
transitive degree	μ_t(G) = 13952

A minimal faithful permutation representation — 3 generators on 141 points:

(1,2,5,7)(3,9,11,16)(4,12,13,8)(6,14,15,10)(17,18)(19,25)(20,22)(21,29)(23,27)(24,28)(26,31)(30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(1,3,4,10,5,11,13,14)(2,6,8,9,7,15,12,16)(18,22)(23,30)(24,29)(25,31);(2,7)(6,15)(8,12)(9,16)(17,19,21,27,20,26,28,32)(18,23,24,25,22,30,29,31)

Conjugacy classes & character table

4142 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₉×#7093, C₁₀₉×#12449, C₁₀₉×#12450, …
maximal normal subgroup of	C₁₀₉×#7093, C₁₀₉×#12449, C₁₀₉×#12450, …
maximal quotient of	C₁₀₉×#8816, C₁₀₉×#9821, C₁₀₉×#9823, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 442);

C109×#1710 #28358964