#14515897

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂×C₃	C₂×#4169
commutator	C₂×C₃×C₉	C₂²×C₉
Frattini, socle, prime radical	C₂×C₃³	C₂×C₃×D₃
Fitting	C₄×#6855	C₂
cosocle	C₂×C₃²×C₉	C₂²×C₃
hypercenter	C₃×C₄	#4169
hypocenter	C₃×C₉	Q₈×C₉
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

207 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 207 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

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

μ_t(G) = 216

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 291);