C₃₁×#89137 #27214038

order	13516
isoclinism	isoclinic class of #89137
automorphism	?
homology	Abelianization (H₁) = C₄×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₁×#89137

Splittings

Fitting, socle, Hall	C₃₁×C₁₀₉ ⋊ C₄
derived, Sylow	C₁₀₉ ⋊ C₄×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃₁	#89137
commutator, hypocenter	C₁₀₉	C₄×C₃₁
Frattini	C₁	G
Fitting, socle	C₃₁×C₁₀₉	C₄
prime radical	C₃₁×D₁₀₉	C₂
cosocle	D₁₀₉	C₂×C₃₁
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₃₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 140
transitive degree	μ_t(G) = 3379

A minimal faithful permutation representation — 2 generators on 140 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13516, 6);

C31×#89137 #27214038