C₃×D₃×C₄²⋊C₃ #11723052

order	864
isoclinism	isoclinic class of D₃×C₄²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃×C₄

Aliases

direct product	C₃×D₃×C₄²⋊C₃
unambiguous semidirect product	C₃⋊(C₂×C₃×C₄²⋊C₃)
unambiguous semidirect product	(C₄²×D₃)⋊C₃²
unambiguous semidirect product	(C₃×C₄²×D₃)⋊C₃

Fitting	C₃²×C₄² ⋊ C₂×C₃
derived	C₃×C₄² ⋊ C₂×C₃²

	subgroup	G/H
center, hypercenter	C₃	D₃×C₄²⋊C₃
commutator, cosocle, hypocenter	C₃×C₄²	C₂×C₃²
Frattini	C₂²	C₃×D₃×A₄
Fitting	C₃²×C₄²	C₂×C₃
socle	C₂²×C₃²	C₂×A₄
LCS	G ▷ C₃×C₄²
UCS	C₁ ◁ C₃

164 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.

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

μ_t(G) = 72

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 3019);