D₃×#15690493 #32914906

order	18486
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×#15690493
unambiguous semidirect product	C₃⋊(C₂×#15690493)

Splittings

Fitting, socle, derived	C₃×C₁₃×C₇₉ ⋊ C₂×C₃
Hall	C₃×#15690493 ⋊ C₂
Hall	C₁₃×C₇₉ ⋊ C₃×D₃
Sylow	C₇₉ ⋊ D₃×C₁₃⋊C₃
Sylow	C₁₃ ⋊ D₃×C₇₉⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₇₉	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₇₉
UCS	C₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 3081

A minimal faithful permutation representation — 2 generators on 95 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)(28,40,48)(31,43,45)(34,46,42)(36,38,39)(41,53,63)(44,56,61)(47,59,58)(49,54,55)(51,64,52)(57,65,72)(60,68,70)(62,66,67)(69,73,77)(71,74,75)(76,78,79)(81,82,84)(83,86,89)(85,88,87)(90,92,91)(94,95);(1,2,4,8,15,25,38,22,32,45,58,67,53,24,36,49,62,71,76,78,68,43,17,3,6,11,18,28,41,54,33,12,19,29,42,55,37,51,50,63,72,77,79,73,56,27,7,13,21,31,44,57,66,46,20,5,9,16,26,39,52,64,35,48,61,70,75,65,40,14,23,34,47,60,69,74,59,30,10)(80,81,83,82,85,89,86,90,92,84,87,91,88)(93,94,95)

Conjugacy classes & character table

1035 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×#20259721, D₃×#20259717, D₃×#20259713, …
maximal normal subgroup of	D₃×#20259721, D₃×#20259717, D₃×#20259713, …
maximal quotient of	Dic₃×#15690493, C₂×D₃×#15690493

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 69);

D3×#15690493 #32914906