D₃×#63544 #13155184

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

C₃³ ⋊ C₂×M₃₂

	subgroup	G/H
center, Frattini, hypercenter	C₈	D₃³
commutator, socle	C₂×C₃³	C₂²×C₈
Fitting, cosocle	C₃³×C₈	C₂³
prime radical	C₂×D₃×C₃⋊D₃	C₈
hypocenter	C₃³	C₂×M₃₂
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₈

510 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

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

μ_t(G) = 96

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 21247);