D₃×#19151040 #46802903

order	34164
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

D₃×#19151040

Splittings

Fitting, socle, derived	C₃×C₁₃×C₇₃ ⋊ C₂²×C₃
Hall	C₃×#15667865 ⋊ C₂²
Hall	C₁₃×C₇₃ ⋊ C₂×C₃×D₃
Sylow	C₇₃ ⋊ C₂×D₃×C₁₃⋊C₃
Sylow	C₁₃ ⋊ D₃×D₇₃⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₇₃	C₂²×C₃
LCS	G ▷ C₃×C₁₃×C₇₃
UCS	C₁

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 89
transitive degree	μ_t(G) = 2847

A minimal faithful permutation representation — 2 generators on 89 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34164, 269);

D3×#19151040 #46802903