C₃×A₄×C₃⋊D₉ #14519247

order	1944
isoclinism	isoclinic class of A₄×C₃⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂×C₃²

Aliases

direct product	C₃×A₄×C₃⋊D₉
unambiguous semidirect product	C₃⋊(C₃×A₄×D₉)

Fitting	C₂²×C₃²×C₉ ⋊ C₂×C₃
derived	C₂²×C₃×C₉ ⋊ C₂×C₃²

	subgroup	G/H
center, hypercenter	C₃	A₄×C₃⋊D₉
commutator, cosocle, hypocenter	C₂²×C₃×C₉	C₂×C₃²
Frattini	C₃	C₃×A₄×C₃⋊D₃
Fitting	C₂²×C₃²×C₉	C₂×C₃
socle	C₂²×C₃³	C₃×D₃
LCS	G ▷ C₂²×C₃×C₉
UCS	C₁ ◁ C₃

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

normal subgroups only

This group has 671 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) = 216

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3641);