D₃×#19150897 #46801418

order	34038
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×#19150897
unambiguous semidirect product	C₃⋊(C₂×#19150897)

Splittings

Fitting, socle, derived	C₃×C₃₁×C₆₁ ⋊ C₂×C₃
Hall	C₃×#19150897 ⋊ C₂
Hall	C₃₁×C₆₁ ⋊ C₃×D₃
Sylow	C₆₁ ⋊ D₃×C₃₁⋊C₃
Sylow	C₃₁ ⋊ D₃×C₆₁⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₁×C₆₁	C₂×C₃
LCS	G ▷ C₃×C₃₁×C₆₁
UCS	C₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 5673

A minimal faithful permutation representation — 2 generators on 95 points:

(2,3)(5,6,8)(7,10,15)(9,13,12)(11,17,24)(14,18,21)(16,22,19)(20,27,30)(23,29,28)(25,31,26)(32,34,33)(36,37,39)(38,41,46)(40,44,43)(42,48,56)(45,51,53)(47,54,50)(49,58,59)(52,61,66)(55,64,63)(57,67,60)(62,72,70)(65,75,77)(68,78,74)(69,73,71)(76,83,81)(79,86,85)(80,84,82)(87,91,89)(88,92,90)(93,95,94);(1,2,3)(4,5,7,11,18,6,9,14,20,27,10,16,23,24,30,17,25,32,31,15,21,28,33,34,22,8,12,19,26,29,13)(35,36,38,42,49,59,70,81,89,94,91,75,51,37,40,45,52,62,73,56,66,77,85,90,83,61,41,47,55,65,76,84,67,46,53,63,74,82,72,48,57,68,79,87,92,78,54,39,43,50,60,71,58,69,80,88,93,95,86,64,44)

Conjugacy classes & character table

1899 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34038, 53);

D3×#19150897 #46801418