C₃×C₃⋊C₈×SL(2,𝔽₃) #13157032

order	1728
automorphism	?
homology	Abelianization (H₁) = C₃²×C₈ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₃⋊C₈×SL(2,𝔽₃)
unambiguous semidirect product	C₃⋊(C₃×C₈×SL(2,𝔽₃))
unambiguous semidirect product	(Q₈×C₃⋊C₈)⋊C₃²
unambiguous semidirect product	(C₃×Q₈×C₃⋊C₈)⋊C₃

C₃×Q₈ ⋊ C₃²×C₈

324 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

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

μ_t(G) = 192

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 23095);