C₂×#10620072 #13049303

order	1296
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, hypercenter	C₂×C₃	A₄×C₃⋊D₃
commutator, cosocle, hypocenter	C₂²×H(3,𝔽₃)	C₂²×C₃
Frattini	C₃	C₂×A₄×C₃⋊D₃
Fitting	C₂³×H(3,𝔽₃)	C₂×C₃
socle	C₂³×C₃	C₃×C₃⋊D₃
prime radical	C₂³×#272	C₃
LCS	G ▷ C₂²×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃

411 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 411 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

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

μ_t(G) = 54

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 3021);