3₋¹⁺²⋊#622 #14518594

order	1944
isoclinism	isoclinic class of 3₋¹⁺²⋊#157
automorphism	?
homology	Abelianization (H₁) = C₃×C₈ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product	3₋¹⁺²⋊#622
unambiguous semidirect product	(C₉⋊#622)⋊C₃

derived	C₃²×C₉ ⋊ C₃×C₈
Sylow	C₃²×3₋¹⁺² ⋊ C₈

222 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.

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

μ_t(G) = 72

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2988);