D₃×#19151039 #46802902

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

Aliases

direct product

D₃×#19151039

Splittings

Fitting, socle, derived	C₃×C₁₃×C₇₃ ⋊ C₂²×C₃
Hall	C₃×#15667864 ⋊ 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)(35,62,63,46,47,76)(37,60,61,49,45,54)(39,41,59,51,52,55)(48,64,73,50,65,79)(53,58,78,66,67,74)(56,83,81,70,71,69)(68,77,84,72,80,88)(75,89,87,85,86,82);(2,3)(4,5,7,6,9,13,10,14,16,8,11,15,12)(17,18,21,27,35,48,49,36,20,24,29,39,53,68,70,52,26,32,40,54,69,82,85,67,34,45,55,57,73,84,89,80,47,64,71,74,76,63,78,83,65,62,77,86,88,79,44,59,60,43,58,75,87,81,61,31,42,30,41,56,72,66,51,38,23,22,28,37,50,46,33,25,19)

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, 268);

D3×#19151039 #46802902