C₂×#10619741 #13048103

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

Aliases

C₂³×C₃×C₉ ⋊ D₃

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₃⋊S₄)⋊C₃
commutator, cosocle, hypocenter	C₂²⋊H(3,𝔽₃)	C₂²×C₃
Frattini	C₃²	C₂×C₃×S₄
Fitting	C₂³×C₃×C₉	D₃
socle	C₂³×C₃	(C₃⋊D₃)⋊C₃
prime radical	C₂×#6258	C₃
LCS	G ▷ C₂²⋊H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃

194 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 26 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, 1821);