C₂×#10620044 #13049275

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

Aliases

C₂³×C₃×C₉ ⋊ D₃

	subgroup	G/H
center, hypercenter	C₂×C₉	C₃⋊S₄
commutator, cosocle, hypocenter	C₂²⋊H(3,𝔽₃)	C₂²×C₃
Frattini	C₃	C₂×C₃×C₃⋊S₄
Fitting	C₂³×C₃×C₉	D₃
socle	C₂³×C₃	C₃×C₃⋊D₃
prime radical	C₂×#6258	C₃
LCS	G ▷ C₂²⋊H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₉

288 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 42 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, 2993);