C₂×C₃⋊(#120⋊C₉) #13147305

order	1728
isoclinism	isoclinic class of C₃⋊(#120⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×C₃⋊(#120⋊C₉)
unambiguous semidirect product	(C₂×C₃)⋊(#120⋊C₉)
unambiguous semidirect product	(C₂×#953)⋊C₉

C₂⁴×C₃ ⋊ C₂²×C₉

678 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.

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

μ_t(G) = 36

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 13368);