C₃×C₅×D₃×C₃⋊D₃ #13108544

order	1620
isoclinism	isoclinic class of D₃×C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×C₅×D₃×C₃⋊D₃
unambiguous semidirect product	(C₃×D₃)⋊(C₃×C₅×D₃)

	subgroup	G/H
center, hypercenter	C₃×C₅	D₃×C₃⋊D₃
commutator, cosocle, hypocenter	C₃³	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃⁴×C₅	C₂²
LCS	G ▷ C₃³
UCS	C₁ ◁ C₃×C₅

448 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

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

μ_t(G) = 180

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 450);