C₃×D₄×(C₃⋊D₃)⋊C₃ #13048849

order	1296
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂³×C₃²

Aliases

direct product	C₃×D₄×(C₃⋊D₃)⋊C₃
unambiguous semidirect product	(D₄×C₃⋊D₃)⋊C₃²
unambiguous semidirect product	(C₃×D₄×C₃⋊D₃)⋊C₃

Fitting	C₃×D₄×H(3,𝔽₃) ⋊ C₂
Sylow	C₃×H(3,𝔽₃) ⋊ C₂×D₄

684 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.

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

μ_t(G) = 72

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2567);