C₁₀₉×#1747 #28359001

order	13952
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₀₉ · Schur multiplier (H₂) = C₄²

Aliases

direct product

C₁₀₉×#1747

Subgroups

	subgroup	G/H
center	C₈×C₁₀₉	C₄²
commutator	C₄	C₂×C₄²×C₁₀₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₉
socle	C₂×C₁₀₉	#376
prime radical	C₂³×C₁₀₉	#41
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₈×C₁₀₉ ◁ G

200 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)(3,11,14,24)(4,8)(5,9)(6,10)(7,13,19,27)(12,23,26,31)(15,20)(16,21)(17,22)(18,25,29,32)(28,30)(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)(2,7,10,19)(4,12)(5,13)(6,14)(8,18,21,29)(9,11,22,24)(15,25)(16,26)(17,27)(20,23,30,31)(28,32);(1,4,5,15,6,16,17,28)(2,8,9,20,10,21,22,30)(3,12,13,25,14,26,27,32)(7,18,11,23,19,29,24,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₉×#11769, C₁₀₉×#11770, C₁₀₉×#11771, …
maximal normal subgroup of	C₁₀₉×#11769, C₁₀₉×#11770, C₁₀₉×#11771, …
maximal quotient of	C₁₀₉×#8137, C₁₀₉×#8138, C₁₀₉×#8139, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 479);

C109×#1747 #28359001