C₁₀₉×#1308 #28358562

order	13952
nilpotency class	3
isoclinism	isoclinic class of #1304
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₀₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₀₉×#1308

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₉	#95
commutator	C₂³	C₄²×C₁₀₉
Frattini, cosocle	C₂×C₄²	C₂²×C₁₀₉
prime radical	C₂³×C₁₀₉	C₄²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₉ ◁ C₂×C₄²×C₁₀₉ ◁ G

122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 141
transitive degree	μ_t(G) = 6976

A minimal faithful permutation representation — 2 generators on 141 points:

(1,2,4,9,6,8,5,10)(3,11,12,16,13,7,14,15)(17,18,20,23,21,24,28,31)(19,25,27,32,26,22,29,30)(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);(1,3,5,12,6,13,4,14)(2,7,10,15,8,11,9,16)(17,19)(18,22,24,25)(20,27)(21,26)(23,30,31,32)(28,29)

Conjugacy classes & character table

2834 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₉×#1308, C₁₀₉×#8124, C₁₀₉×#8125, …
maximal normal subgroup of	C₂×C₁₀₉×#1308, C₁₀₉×#8124, C₁₀₉×#8125, …
maximal quotient of	C₁₀₉×#7033, C₁₀₉×#7041, C₁₀₉×#7048, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 40);

C109×#1308 #28358562