D₃×#15667865 #30685204

order	17082
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×#15667865
unambiguous semidirect product	C₃⋊(C₂×#15667865)

Splittings

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

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₇₃	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₇₃
UCS	C₁

36 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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×#19151048, D₃×#19151044, D₃×#19151040, …
maximal normal subgroup of	D₃×#19151048, D₃×#19151044, D₃×#19151040, …
maximal quotient of	Dic₃×#15667865, C₂×D₃×#15667865

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17082, 66);

D3×#15667865 #30685204