C₃×C₉⋊GL(2,𝔽₃) #13048384

order	1296
isoclinism	isoclinic class of C₉⋊#226
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₃

Aliases

Fitting	C₃×Q₈×C₉ ⋊ D₃
derived	C₉×SL(2,𝔽₃) ⋊ C₂×C₃

	subgroup	G/H
center, hypercenter	C₂×C₃	C₉⋊S₄
commutator, cosocle, hypocenter	C₉×SL(2,𝔽₃)	C₂×C₃
Frattini	C₂×C₃	C₃×C₃⋊S₄
Fitting	C₃×Q₈×C₉	D₃
socle	C₂×C₃²	C₃⋊S₄
LCS	G ▷ C₉×SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃

199 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 199 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.

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

μ_t(G) = 144

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2102);