C₁₀₉×#3125 #28360379

order	13952
nilpotency class	3
isoclinism	isoclinic class of #3008
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₀₉×#3125

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₀₉
prime radical	#449×C₁₀₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₉ ◁ #117×C₁₀₉ ◁ G

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 133
transitive degree	μ_t(G) = 6976

A minimal faithful permutation representation — 4 generators on 133 points:

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

Conjugacy classes & character table

3488 conjugacy classes. The character table is too large to display.

Relationships

maximal quotient of

C₁₀₉×#20746, C₁₀₉×#21126, C₁₀₉×#21127, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 1857);

C109×#3125 #28360379