C₄⋊((3₋¹⁺²⋊C₉)⋊C₂) #14516139

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

Fitting	C₄×3₋¹⁺²⋊C₉ ⋊ C₂
Sylow	3₋¹⁺²⋊C₉ ⋊ D₄

289 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 289 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

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

μ_t(G) = 324

Polycyclic presentation:

2^3,3^5|b^2=c,d^3=g,e^3=g,b^a=bc,d^a=d^2g^2,e^a=e^2g^2,f^a=fh^2,g^a=g^2,h^a=h^2,e^d=ef,f^e=fh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 533);