C₂×D₉×AGL(1,ℤ/9) #14518287

order	1944
isoclinism	isoclinic class of D₉×AGL(1,ℤ/9)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂×D₉×AGL(1,ℤ/9)
unambiguous semidirect product	D₉⋊(C₂×C₃×D₉)
unambiguous semidirect product	(C₉×AGL(1,ℤ/9))⋊C₂²
unambiguous semidirect product	(D₉×3₋¹⁺²)⋊C₂²
unambiguous semidirect product	#92299⋊C₂²

	subgroup	G/H
center, hypercenter	C₂	D₉×AGL(1,ℤ/9)
commutator, cosocle, hypocenter	C₉²	C₂³×C₃
Frattini	C₃²	C₂×C₃×D₃²
Fitting	C₂×C₉×3₋¹⁺²	C₂²
socle	C₂×C₃²	C₃×D₃²
LCS	G ▷ C₉²
UCS	C₁ ◁ C₂

388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

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

μ_t(G) = 108

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2681);