C₂×D₃×H(3,𝔽₃) #66447

order	324
isoclinism	isoclinic class of D₃×H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃²

Aliases

direct product	C₂×D₃×H(3,𝔽₃)
unambiguous semidirect product	C₃⋊(C₂²×H(3,𝔽₃))
unambiguous semidirect product	(C₂×C₃)⋊(C₂×H(3,𝔽₃))
unambiguous semidirect product	(C₂×C₃²×D₃)⋊C₃

Fitting	C₂×C₃×H(3,𝔽₃) ⋊ C₂
Sylow	C₃×H(3,𝔽₃) ⋊ C₂²

144 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 2 generators on 14 points:

(4,5)(6,7,10)(8,9,13)(11,12,14);(1,2)(3,4,5)(7,9,12)(10,14,13)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 139);