C₄⋊#66343 #13047069

order	1296
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₉

Aliases

Fitting	C₄×C₉² ⋊ C₄
Sylow	C₉² ⋊ C₄⋊C₄

119 conjugacy classes of subgroups.

μ_t(G) = 72

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 787);