D₃×#6188 #13048232

order	1296
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₃×#157
commutator, hypocenter	C₃×H(3,𝔽₃)	C₂×C₈
Fitting	C₂×C₃×H(3,𝔽₃)	C₂×C₄
socle	C₂×C₃²	C₂×#157
prime radical	C₂×D₃×H(3,𝔽₃)	C₄
cosocle	C₃×#1084	C₂²
LCS	G ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃

158 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 29 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(1296, 1950);