C₂²×D₉⋊SL(2,𝔽₃) #13164576

order	1728
isoclinism	isoclinic class of #88614
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₂²×D₉⋊SL(2,𝔽₃)
unambiguous semidirect product	D₉⋊(C₂²×SL(2,𝔽₃))

Fitting	C₂²×Q₈×C₉ ⋊ C₂×C₃
derived	Q₈×C₉ ⋊ C₂³×C₃

	subgroup	G/H
center, hypercenter	C₂³	D₉⋊A₄
commutator, cosocle, hypocenter	Q₈×C₉	C₂³×C₃
Frattini	C₂×C₃	C₂²×D₃×A₄
Fitting	C₂²×Q₈×C₉	C₂×C₃
socle	C₂³×C₃	D₃×A₄
LCS	G ▷ Q₈×C₉
UCS	C₁ ◁ C₂³

861 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 861 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.

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

μ_t(G) = 288

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 30639);