C₂²×C₃×#4208 #14519367

order	1944
isoclinism	isoclinic class of #272
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂²×C₃×#4208

Fitting	C₂²×C₃×#737 ⋊ C₂
Sylow	C₃×#737 ⋊ C₂³

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₉	C₃⋊D₃
commutator, cosocle, hypocenter	H(3,𝔽₃)	C₂³×C₃²
Frattini	C₃	C₂²×C₃²×C₃⋊D₃
Fitting	C₂²×C₃×#737	C₂
socle	C₂²×C₃²	C₃×C₃⋊D₃
prime radical	C₂²×C₃×#272	C₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂²×C₃×C₉

1356 conjugacy classes of subgroups; only the 266 normal subgroups are shown.

normal subgroups only

This group has 1356 conjugacy classes of subgroups — too many to draw. Only its 266 normal subgroups are shown.

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

μ_t(G) = 324

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3761);