Dic₆×#733 #14517373

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product	Dic₆×#733
unambiguous semidirect product	C₃⋊(Q₈×#733)

	subgroup	G/H
center	C₂×C₃	C₂×D₃×H(3,𝔽₃)
commutator, prime radical, cosocle	C₂×C₃³	C₂²×C₃²
Frattini	C₂×C₃²	C₂×C₃²×D₃
Fitting	C₃×C₄×#733	C₂
socle	C₂×C₃²	C₂²×H(3,𝔽₃)
hypercenter	C₄×#733	D₃
hypocenter	C₃	Q₈×#733
LCS	G ▷ C₂×C₃³ ▷ C₃² ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃²×C₄ ◁ C₄×#733

216 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

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

μ_t(G) = 216

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1767);