Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Sylow | H(5,𝔽3) ⋊ Q8 |
153 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2^2,3^2,2,3^3|a^2=e,b^2=e,b^a=be,f^a=gh^2,g^a=f^2,f^b=fg^2,g^b=f^2g^2h,d^c=dh^2,f^e=f^2h^2,g^e=g^2h,g^f=gh64 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3543);