#14517986

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

No aliases for this group.

	subgroup	G/H
center	C₃	C₃×(C₃⋊S₄)⋊C₃
commutator, cosocle, hypocenter	C₂²⋊H(3,𝔽₃)	C₂×C₃²
Frattini	C₃²	C₃²×S₄
Fitting	C₂²×C₃×3₋¹⁺²	D₃
socle	C₂²×C₃	C₃×(C₃⋊D₃)⋊C₃
hypercenter	C₃²	(C₃⋊S₄)⋊C₃
LCS	G ▷ C₂²⋊H(3,𝔽₃)
UCS	C₁ ◁ C₃ ◁ C₃²

223 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 223 conjugacy classes of subgroups — too many to draw. Only its 30 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:

2,3^5,2^2|c^3=f^2,d^a=d^2,e^a=e^2f,g^a=gh,c^b=cf^2,d^c=de^2,e^d=ef,g^d=h,h^d=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2380);