C₁₀₉×#1924 #28359178

order	13952
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₉×#1924

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₀₉	C₂³
commutator	C₂³	C₂²×C₄×C₁₀₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₉
socle	C₂³×C₁₀₉	C₂²×C₄
prime radical	C₂⁴×C₁₀₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₉ ◁ G

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 125
transitive degree	μ_t(G) = 6976

A minimal faithful permutation representation — 3 generators on 125 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₀₉×#1924, C₁₀₉×#21047, C₁₀₉×#21048, …
maximal normal subgroup of	C₂×C₁₀₉×#1924, C₁₀₉×#21047, C₁₀₉×#21048, …
maximal quotient of	C₁₀₉×#9545, C₁₀₉×#9546, C₁₀₉×#9547, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 656);

C109×#1924 #28359178