C₂×D₃×C₉⋊D₉ #14518310

order	1944
isoclinism	isoclinic class of D₃×C₉⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³×C₉

Aliases

C₂×D₃×C₉⋊D₉

Fitting	C₂×C₃×C₉² ⋊ C₂²
derived, Sylow	C₃×C₉² ⋊ C₂³

	subgroup	G/H
center, hypercenter	C₂	D₃×C₉⋊D₉
commutator, cosocle, hypocenter	C₃×C₉²	C₂³
Frattini	C₃²	C₂×D₃×C₃⋊D₃
Fitting	C₂×C₃×C₉²	C₂²
socle	C₂×C₃³	C₂×C₃⋊D₃
LCS	G ▷ C₃×C₉²
UCS	C₁ ◁ C₂

936 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.

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

μ_t(G) = 324

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2704);