C₂₉×#90673 #27189953

order	13108
isoclinism	isoclinic class of #90673
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₂₉×#90673

Splittings

Fitting, socle, Hall	C₂₉×C₁₁₃ ⋊ C₄
derived, Sylow	C₁₁₃ ⋊ C₄×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	#90673
commutator, hypocenter	C₁₁₃	C₄×C₂₉
Frattini	C₁	G
Fitting, socle	C₂₉×C₁₁₃	C₄
prime radical	C₂₉×D₁₁₃	C₂
cosocle	D₁₁₃	C₂×C₂₉
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₂₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 142
transitive degree	μ_t(G) = 3277

A minimal faithful permutation representation — 2 generators on 142 points:

(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,98)(74,96,97,112)(78,100,101,110)(82,104,105,107)(86,108,109,103)(90,111,106,99)(92,113,102,95)(114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142);(1,2,5,10,19,32,49,70,93,97,73,52,35,22,13,6,11,20,33,50,71,95,96,68,92,101,77,56,39,26,15,24,37,54,75,99,100,72,47,67,90,105,81,60,43,28,41,58,79,103,104,76,51,30,46,65,86,109,85,64,45,62,83,107,108,80,55,34,17,29,44,61,82,106,89,66,87,110,111,84,59,38,21,8,16,27,40,57,78,102,91,112,113,88,63,42,25,12,3,7,14,23,36,53,74,98,94,69,48,31,18,9,4)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13108, 6);

C29×#90673 #27189953