#13091470

order	1458
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃²

Aliases

No aliases for this group.

	subgroup	G/H
center	C₃	C₃×C₃⋊((C₃⋊D₃)⋊C₃)
commutator, cosocle, hypocenter	C₃×H(3,𝔽₃)	C₂×C₃²
Frattini, socle	C₃²	C₃²×C₃⋊D₃
Fitting	#10624881	C₂
prime radical	C₃×C₃⋊#272	C₃
hypercenter	C₃²	C₃⋊((C₃⋊D₃)⋊C₃)
LCS	G ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₃ ◁ C₃²

434 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

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

μ_t(G) = 54

Polycyclic presentation:

2,3^6|b^3=f,c^a=c^2e^2,d^a=d^2,g^a=g^2,c^b=cf,d^b=dg,e^b=ef,d^c=df

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 1544);