#13165137

order	1728
isoclinism	isoclinic class of AGL(1,𝔽₉)⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₃³ ⋊ #340

	subgroup	G/H
center, Frattini, hypercenter	C₂²	AGL(1,𝔽₉)⋊D₃
commutator	C₃×#157	C₄²
Fitting, socle	C₂²×C₃³	SD₁₆
prime radical	C₂²×C₃×C₃⋊D₃	D₄
cosocle	C₂²×C₃×#157	C₂²
hypocenter	C₃³	#340
LCS	G ▷ C₃×#157 ▷ C₃×C₃⋊D₃ ▷ C₃³
UCS	C₁ ◁ C₂²

298 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

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

μ_t(G) = 192

Polycyclic presentation:

2^6,3^3|a^2=e,b^2=cd,c^2=f,b^a=bc,c^a=cf,g^a=g^2,h^a=h^2,h^b=h^2i^2,i^b=hi^2,h^c=i^2,i^c=h,h^f=h^2,i^f=i^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 31200);