C₂×C₃×#64264 #13181380

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂²×C₃²×Q₈ ⋊ D₃

	subgroup	G/H
center	C₂²×C₃	C₂×C₃⋊S₄
commutator, cosocle, hypocenter	C₃×SL(2,𝔽₃)	C₂³×C₃
Frattini	C₂	C₂²×C₃×C₃⋊S₄
Fitting	C₂²×C₃²×Q₈	D₃
socle	C₂²×C₃²	C₂×S₄
hypercenter	C₂³×C₃	C₃⋊S₄
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂²×C₃ ◁ C₂³×C₃

971 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 971 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

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

μ_t(G) = 96

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47443);