C₃×D₄₄₂₉ #40997986

order	26574
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×D₄₄₂₉

Splittings

Fitting, socle, Hall	C₃×C₄₃×C₁₀₃ ⋊ C₂
derived, Hall	C₄₃×C₁₀₃ ⋊ C₂×C₃
Hall	C₃×C₁₀₃ ⋊ D₄₃
Hall	C₃×C₄₃ ⋊ D₁₀₃
Sylow	C₁₀₃ ⋊ C₃×D₄₃
Sylow	C₄₃ ⋊ C₃×D₁₀₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₄₄₂₉
commutator, cosocle, hypocenter	C₄₃×C₁₀₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₄₃×C₁₀₃	C₂
LCS	G ▷ C₄₃×C₁₀₃
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 149
transitive degree	μ_t(G) = 13287

A minimal faithful permutation representation — 2 generators on 149 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)(47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149);(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)(48,149)(49,148)(50,147)(51,146)(52,145)(53,144)(54,143)(55,142)(56,141)(57,140)(58,139)(59,138)(60,137)(61,136)(62,135)(63,134)(64,133)(65,132)(66,131)(67,130)(68,129)(69,128)(70,127)(71,126)(72,125)(73,124)(74,123)(75,122)(76,121)(77,120)(78,119)(79,118)(80,117)(81,116)(82,115)(83,114)(84,113)(85,112)(86,111)(87,110)(88,109)(89,108)(90,107)(91,106)(92,105)(93,104)(94,103)(95,102)(96,101)(97,100)(98,99)

Conjugacy classes & character table

6648 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26574, 8);

C3×D4429 #40997986