C₂×#11722374 #13164462

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

Aliases

Fitting	C₂×C₉×#41 ⋊ D₃
derived	C₉×SL(2,𝔽₃) ⋊ C₂³

	subgroup	G/H
center	C₂²	C₂×C₉⋊S₄
commutator, cosocle, hypocenter	C₉×SL(2,𝔽₃)	C₂³
Frattini	C₂×C₃	C₂²×C₃⋊S₄
Fitting	C₂×C₉×#41	D₃
socle	C₂²×C₃	C₂×C₃⋊S₄
hypercenter	C₂×C₄	C₉⋊S₄
LCS	G ▷ C₉×SL(2,𝔽₃)
UCS	C₁ ◁ C₂² ◁ C₂×C₄

679 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 679 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

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

μ_t(G) = 288

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 30525);