D₃×#19151043 #46802891

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

Aliases

direct product

D₃×#19151043

Splittings

Fitting, socle, derived	C₃×C₁₃×C₇₃ ⋊ C₂²×C₃
Hall	C₃×#15667864 ⋊ C₂²
Hall	C₁₃×C₇₃ ⋊ C₂×C₃×D₃
Sylow	C₇₃ ⋊ D₃×D₁₃⋊C₃
Sylow	C₁₃ ⋊ C₂×D₃×C₇₃⋊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)(5,9,10,6,7,11)(8,15,14,12,13,16)(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)(41,53,66)(44,56,63)(47,54,60)(50,61,58)(52,64,55)(57,69,78)(59,70,75)(62,74,73)(65,76,71)(67,79,68)(72,82,85)(77,84,83)(80,86,81)(87,89,88);(2,3)(4,5,8,7,11,14,13,15,16,10,9,12,6)(17,18,20,24,31,41,54,33,19,22,27,34,44,57,70,43,23,29,37,47,59,72,82,56,30,39,50,62,66,78,85,69,40,52,65,77,79,51,63,75,53,67,80,87,86,64,38,48,60,73,83,88,89,76,49,28,35,45,58,71,81,84,61,36,21,25,32,42,55,68,74,46,26)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34164, 257);

D3×#19151043 #46802891