C₂²×D₃×AGL(1,ℤ/9) #13049316

order	1296
isoclinism	isoclinic class of D₃×AGL(1,ℤ/9)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product	C₂²×D₃×AGL(1,ℤ/9)
unambiguous semidirect product	D₉⋊(C₂²×C₃×D₃)
unambiguous semidirect product	(D₃×D₉)⋊(C₂²×C₃)
unambiguous semidirect product	(C₃×AGL(1,ℤ/9))⋊C₂³
unambiguous semidirect product	(D₃×3₋¹⁺²)⋊C₂³
unambiguous semidirect product	(C₃⋊AGL(1,ℤ/9))⋊C₂³

	subgroup	G/H
center, hypercenter	C₂²	D₃×AGL(1,ℤ/9)
commutator, cosocle, hypocenter	C₃×C₉	C₂⁴×C₃
Frattini	C₃	C₂²×C₃×D₃²
Fitting	C₂²×C₃×3₋¹⁺²	C₂²
socle	C₂²×C₃²	C₂×C₃×D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₂²

958 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 229 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(1296, 3034);