C₂×C₃⋊D₃×#226 #13180752

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

Aliases

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊D₃×S₄
commutator, cosocle, hypocenter	C₃²×SL(2,𝔽₃)	C₂³
Frattini	C₂	C₂×C₃⋊D₃×S₄
Fitting	C₂×C₃²×Q₈	C₂×D₃
socle	C₂²×C₃²	C₂×S₄
prime radical	C₂×C₃⋊D₃×SL(2,𝔽₃)	C₂
LCS	G ▷ C₃²×SL(2,𝔽₃)
UCS	C₁ ◁ C₂²

1022 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 97 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, 46815);