#13046499

order	1296
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, hypercenter	C₂²	#4178⋊C₂
commutator	C₂×#732	C₂×C₄
Frattini	C₂²×C₃²	D₃²
Fitting, prime radical, cosocle	C₂²×#732	C₂²
socle	C₂²×C₃	((C₃⋊D₃)⋊C₃)⋊C₂
hypocenter	#732	C₄⋊C₄
LCS	G ▷ C₂×#732 ▷ #732
UCS	C₁ ◁ C₂²

154 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

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

μ_t(G) = 432

Polycyclic presentation:

2^4,3^4|a^2=d,b^2=c,e^3=h,b^a=bd,f^a=f^2,g^a=g^2h,e^b=e^2h^2,g^b=g^2,h^b=h^2,f^e=fg,g^f=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 217);