C₃×D₄₃₄₃ #39907577

order	26058
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₄₃₄₃
unambiguous semidirect product	C₁₀₁⋊(C₃×D₄₃)

Splittings

Fitting, socle, Hall	C₃×C₄₃×C₁₀₁ ⋊ C₂
derived, Hall	C₄₃×C₁₀₁ ⋊ C₂×C₃
Hall	C₃×C₁₀₁ ⋊ D₄₃
Hall	C₃×C₄₃ ⋊ D₁₀₁
Sylow	C₁₀₁ ⋊ C₃×D₄₃
Sylow	C₄₃ ⋊ C₃×D₁₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₄₃₄₃
commutator, cosocle, hypocenter	C₄₃×C₁₀₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₄₃×C₁₀₁	C₂
LCS	G ▷ C₄₃×C₁₀₁
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 147
transitive degree	μ_t(G) = 13029

A minimal faithful permutation representation — 2 generators on 147 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46)(47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147);(5,46)(6,45)(7,44)(8,43)(9,42)(10,41)(11,40)(12,39)(13,38)(14,37)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(48,147)(49,146)(50,145)(51,144)(52,143)(53,142)(54,141)(55,140)(56,139)(57,138)(58,137)(59,136)(60,135)(61,134)(62,133)(63,132)(64,131)(65,130)(66,129)(67,128)(68,127)(69,126)(70,125)(71,124)(72,123)(73,122)(74,121)(75,120)(76,119)(77,118)(78,117)(79,116)(80,115)(81,114)(82,113)(83,112)(84,111)(85,110)(86,109)(87,108)(88,107)(89,106)(90,105)(91,104)(92,103)(93,102)(94,101)(95,100)(96,99)(97,98)

Conjugacy classes & character table

6519 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26058, 5);

C3×D4343 #39907577