C₂²×C₃²×GL(2,𝔽₃) #13181358

order	1728
isoclinism	isoclinic class of #226
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂³×C₃

Aliases

Fitting	C₂²×C₃²×Q₈ ⋊ D₃
derived	SL(2,𝔽₃) ⋊ C₂³×C₃²

	subgroup	G/H
center, socle, hypercenter	C₂³×C₃²	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂³×C₃²
Frattini	C₂	C₂²×C₃²×S₄
Fitting	C₂²×C₃²×Q₈	D₃
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂³×C₃²

1446 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1446 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.

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

μ_t(G) = 288

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

maximal subgroup of	C₂²×C₃²×AGL(2,𝔽₃)
maximal quotient of	C₂²×C₃²×AGL(2,𝔽₃)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47421);