D₃×#19154249 #46856098

order	35028
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

D₃×#19154249

Splittings

Fitting, socle, derived	C₃×C₇×C₁₃₉ ⋊ C₂²×C₃
Hall	C₃×#15668589 ⋊ C₂²
Hall	C₇×C₁₃₉ ⋊ C₂×C₃×D₃
Sylow	C₁₃₉ ⋊ D₃×AGL(1,𝔽₇)
Sylow	C₇ ⋊ C₂×D₃×C₁₃₉⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₃₉	C₂²×C₃
LCS	G ▷ C₃×C₇×C₁₃₉
UCS	C₁

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 149
transitive degree	μ_t(G) = 2919

A minimal faithful permutation representation — 2 generators on 149 points:

(1,2,3)(5,8,9,6,7,10)(12,13,15)(14,17,22)(16,20,19)(18,24,32)(21,27,29)(23,30,26)(25,34,45)(28,37,42)(31,40,39)(33,43,36)(35,47,61)(38,50,58)(41,53,55)(44,56,52)(46,59,49)(48,63,80)(51,66,77)(54,69,74)(57,72,71)(60,75,68)(62,78,65)(64,82,101)(67,85,98)(70,83,95)(73,90,92)(76,93,89)(79,96,87)(81,99,84)(86,104,119)(88,105,116)(91,109,113)(94,111,110)(97,114,108)(100,117,106)(102,120,103)(107,123,132)(112,126,127)(115,128,125)(118,130,124)(121,133,122)(129,138,137)(131,139,136)(134,141,135)(140,145,144)(142,146,143)(147,149,148);(2,3)(4,5,7,10,9,8,6)(11,12,14,18,25,35,48,64,83,50,24,33,44,57,73,91,101,119,132,104,63,81,100,118,131,140,141,117,78,45,58,74,92,110,125,136,143,145,128,93,56,30,15,19,26,36,49,65,84,103,109,69,37,17,23,31,41,54,70,88,107,123,85,47,62,79,97,115,129,133,99,61,77,95,113,127,137,144,148,149,139,114,75,43,22,29,39,52,68,87,106,122,126,90,53,27,13,16,21,28,38,51,67,86,105,66,34,46,60,76,94,112,120,80,98,116,82,102,121,134,142,147,146,130,96,59,32,42,55,71,89,108,124,135,138,111,72,40,20)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35028, 134);

D3×#19154249 #46856098