C₂×D₃×AΓL(1,𝔽₉) #13181797

order	1728
isoclinism	isoclinic class of D₃×AΓL(1,𝔽₉)
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting, socle	C₂×C₃³ ⋊ C₂×SD₁₆
Sylow	C₃³ ⋊ C₂²×SD₁₆

762 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 48

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47860);

direct product	C₂×D₃×AΓL(1,𝔽₉)
unambiguous semidirect product	(D₃×AGL(1,𝔽₉))⋊C₂²
unambiguous semidirect product	(C₃×AΓL(1,𝔽₉))⋊C₂²
unambiguous semidirect product	#89091⋊C₂²
unambiguous semidirect product	#89092⋊C₂²
unambiguous semidirect product	(AGL(1,𝔽₉)⋊D₃)⋊C₂²
unambiguous semidirect product	(D₃×PSU(3,𝔽₂))⋊C₂²