C₂×#64265⋊C₃ #13164427

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

Aliases

direct product	C₂×#64265⋊C₃
unambiguous semidirect product	(C₂×#64265)⋊C₃

	subgroup	G/H
center	C₂²	C₂×(C₃⋊S₄)⋊C₃
commutator, cosocle, hypocenter	C₃×SL(2,𝔽₃)	C₂³×C₃
Frattini	C₂×C₃	C₂²×C₃×S₄
Fitting	C₂×C₃²×#41	D₃
socle	C₂²×C₃	C₂×C₃×S₄
prime radical	C₂×#41⋊H(3,𝔽₃)	C₂
hypercenter	C₂×C₄	(C₃⋊S₄)⋊C₃
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂² ◁ C₂×C₄

578 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 71 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, 30490);