C₃×A₄×#226 #13180314

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×A₄×#226
unambiguous semidirect product	(C₂²×#226)⋊C₃²
unambiguous semidirect product	(C₂²×C₃×#226)⋊C₃

	subgroup	G/H
center, hypercenter	C₂×C₃	A₄×S₄
commutator, cosocle, hypocenter	C₂²×SL(2,𝔽₃)	C₂×C₃²
Frattini	C₂	C₃×A₄×S₄
Fitting	C₂²×C₃×Q₈	C₃×D₃
socle	C₂³×C₃	C₃×S₄
prime radical	C₃×A₄×SL(2,𝔽₃)	C₂
LCS	G ▷ C₂²×SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃

299 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 299 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

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

μ_t(G) = 144

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46377);