Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D31)⋊C16 |
| Fitting | C2×C16×C31 ⋊ C2 |
| Sylow | C31 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^6,31|a^2=d,d^2=e,e^2=f,b^a=bc,g^b=g^30520 conjugacy classes — view the full character table.
| maximal subgroup of | D31×C22⋊C16, C2×(C2×D31)⋊C16, #16847320, … |
| maximal normal subgroup of | D31×C22⋊C16, C2×(C2×D31)⋊C16, #16847320, … |
| maximal quotient of | #16843634, #16843650, #16843665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 328);