D₃×#20262033 #49153309

order	37386
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×#20262033
unambiguous semidirect product	C₃⋊(C₂×#20262033)

Splittings

Fitting, socle, derived	C₃×C₃₁×C₆₇ ⋊ C₂×C₃
Hall	C₃×#20262033 ⋊ C₂
Hall	C₃₁×C₆₇ ⋊ C₃×D₃
Sylow	C₆₇ ⋊ D₃×C₃₁⋊C₃
Sylow	C₃₁ ⋊ D₃×C₆₇⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₁×C₆₇	C₂×C₃
LCS	G ▷ C₃×C₃₁×C₆₇
UCS	C₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 101
transitive degree	μ_t(G) = 6231

A minimal faithful permutation representation — 2 generators on 101 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)(49,58,69)(52,61,66)(55,64,63)(57,67,60)(59,71,83)(62,73,81)(65,76,78)(68,79,75)(70,82,72)(74,86,93)(77,87,92)(80,90,89)(84,94,85)(88,95,99)(91,96,98)(97,100,101);(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)(35,36,38,42,49,59,67,46,53,63,75,71,84,94,69,81,92,98,95,73,48,57,68,80,91,97,96,76,51,37,40,45,52,62,74,79,54,39,43,50,60,72,85,82,56,66,78,89,86,58,70,83,93,99,101,100,87,61,41,47,55,65,77,88,90,64,44)

Conjugacy classes & character table

2085 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37386, 53);

D3×#20262033 #49153309