C₂³×C₃×D₃×A₄ #13181859

order	1728
isoclinism	isoclinic class of D₃×A₄
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃² · Schur multiplier (H₂) = C₂⁷×C₃

Aliases

direct product	C₂³×C₃×D₃×A₄
unambiguous semidirect product	C₃⋊(C₂⁴×C₃×A₄)
unambiguous semidirect product	(C₂×C₃)⋊(C₂³×C₃×A₄)

Fitting, socle	C₂⁵×C₃² ⋊ C₂×C₃
derived	C₂²×C₃ ⋊ C₂⁴×C₃²

	subgroup	G/H
center, hypercenter	C₂³×C₃	D₃×A₄
commutator, cosocle, hypocenter	C₂²×C₃	C₂⁴×C₃²
Frattini	C₁	G
Fitting, socle	C₂⁵×C₃²	C₂×C₃
LCS	G ▷ C₂²×C₃
UCS	C₁ ◁ C₂³×C₃

5566 conjugacy classes of subgroups; only the 664 normal subgroups are shown.

normal subgroups only

This group has 5566 conjugacy classes of subgroups — too many to draw. Only its 664 normal subgroups are shown.

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

μ_t(G) = 144

288 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47922);