C₁₀₉×#2070 #28359324

order	13952
nilpotency class	3
isoclinism	isoclinic class of #2069
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₉×#2070

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₉	#396
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₉
prime radical	C₂³×C₁₀₉	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₉ ◁ C₂²×C₄×C₁₀₉ ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 141
transitive degree	μ_t(G) = 3488

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

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

Conjugacy classes & character table

2507 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₀₉×#2070, C₁₀₉×#23622, C₁₀₉×#24808, …
maximal normal subgroup of	C₂×C₁₀₉×#2070, C₁₀₉×#23622, C₁₀₉×#24808, …
maximal quotient of	C₁₀₉×#10604, C₁₀₉×#10606, C₁₀₉×#10608, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 802);

C109×#2070 #28359324