C₁₀₉×#1398 #28358652

order	13952
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₀₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₀₉×#1398

Subgroups

	subgroup	G/H
center	C₈×C₁₀₉	C₄²
commutator	C₄	C₄×C₈×C₁₀₉
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₀₉
socle	C₂×C₁₀₉	#346
prime radical	C₂²×C₁₀₉	M₃₂
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₈×C₁₀₉ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₀₉×#7333, C₁₀₉×#7389, C₁₀₉×#7390, …
maximal normal subgroup of	C₁₀₉×#7333, C₁₀₉×#7389, C₁₀₉×#7390, …
maximal quotient of	C₁₀₉×#7330, C₁₀₉×#7332, C₁₀₉×#7466, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 130);

C109×#1398 #28358652