#13048233

order	1296
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₃×#157
commutator, hypocenter	C₃×H(3,𝔽₃)	C₂×C₈
Fitting	C₂×C₃×H(3,𝔽₃)	C₂×C₄
socle	C₂×C₃²	C₂×#157
prime radical	C₂×C₃⋊#272	C₄
cosocle	C₃×#1084	C₂²
LCS	G ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃

170 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.

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

μ_t(G) = 144

Polycyclic presentation:

2^4,3^4|a^2=d,b^2=c,c^2=d,g^a=g^2,e^b=ef,f^b=ef^2h^2,e^c=e^2,f^c=f^2h,f^e=fh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1951);