C₂×C₃×C₄×AGL(1,𝔽₉) #13180925

order	1728
isoclinism	isoclinic class of AGL(1,𝔽₉)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄×C₈ · Schur multiplier (H₂) = C₂²×C₄

Aliases

394 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.

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

μ_t(G) = 192

maximal subgroup of	C₂×C₃×AGL(1,𝔽₅)×AGL(1,𝔽₉), C₄×AGL(1,𝔽₇)×AGL(1,𝔽₉), C₂×C₃×C₄×AΓL(1,𝔽₉)
maximal normal subgroup of	C₂×C₃×C₄×AΓL(1,𝔽₉)
maximal quotient of	C₂×C₃×AGL(1,𝔽₅)×AGL(1,𝔽₉), C₄×AGL(1,𝔽₇)×AGL(1,𝔽₉)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46988);