D₃×#19097154 #44446128

order	29718
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×#19097154
unambiguous semidirect product	C₃⋊(C₂×#19097154)

Splittings

Fitting, socle, derived	C₃×C₁₃×C₁₂₇ ⋊ C₂×C₃
Hall	C₃×#19097154 ⋊ C₂
Hall	C₁₃×C₁₂₇ ⋊ C₃×D₃
Sylow	C₁₂₇ ⋊ D₃×C₁₃⋊C₃
Sylow	C₁₃ ⋊ D₃×C₁₂₇⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₁₂₇	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₁₂₇
UCS	C₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 143
transitive degree	μ_t(G) = 4953

A minimal faithful permutation representation — 2 generators on 143 points:

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

Conjugacy classes & character table

1659 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29718, 65);

D3×#19097154 #44446128