A₄×(C₃⋊D₃)⋊C₃ #10620063

order	648
isoclinism	isoclinic class of A₄×(C₃⋊D₃)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂×C₃²

Aliases

direct product	A₄×(C₃⋊D₃)⋊C₃
unambiguous semidirect product	((C₃⋊D₃)⋊A₄)⋊C₃
unambiguous semidirect product	(C₂²×(C₃⋊D₃)⋊C₃)⋊C₃
unambiguous semidirect product	(A₄×C₃⋊D₃)⋊C₃

Fitting	C₂²×H(3,𝔽₃) ⋊ C₂×C₃
derived	C₂²×C₃² ⋊ C₂×C₃²

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂²×C₃²	C₂×C₃²
Frattini	C₃	C₃×D₃×A₄
Fitting	C₂²×H(3,𝔽₃)	C₂×C₃
socle	C₂²×C₃	C₃²×D₃
LCS	G ▷ C₂²×C₃²
UCS	C₁

146 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.

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

μ_t(G) = 36

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 582);