C₂²×C₃×C₃⋊(C₃⋊D₉) #14519372

order	1944
isoclinism	isoclinic class of C₃⋊(C₃⋊D₉)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³×C₃³

Aliases

	subgroup	G/H
center, hypercenter	C₂²×C₃	C₃⋊(C₃⋊D₉)
commutator, cosocle, hypocenter	C₃²×C₉	C₂³×C₃
Frattini	C₃	C₂²×C₃×C₃⋊(C₃⋊D₃)
Fitting	C₂²×C₃³×C₉	C₂
socle	C₂²×C₃⁴	D₃
LCS	G ▷ C₃²×C₉
UCS	C₁ ◁ C₂²×C₃

2340 conjugacy classes of subgroups; only the 522 normal subgroups are shown.

normal subgroups only

This group has 2340 conjugacy classes of subgroups — too many to draw. Only its 522 normal subgroups are shown.

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

μ_t(G) = 648

504 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3766);