Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | #6900 ⋊ Q8 |
312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^2,3,2,3^4|a^2=d,b^2=d,e^3=h,f^3=g,b^a=bd,e^a=e^2h^2,f^a=f^2g^2,g^a=g^2,h^a=h^2,e^c=eh^2,f^c=fg^2111 conjugacy classes — view the full character table.
| maximal subgroup of | #72268689, Q8×#92314, #72268708 |
| maximal normal subgroup of | #72268689, Q8×#92314, #72268708 |
| maximal quotient of | #72268686, #72268698 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1956);