Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C16×C31 ⋊ C2 |
| Sylow | C31 ⋊ #359 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^6,31|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^30,c^b=ce,e^b=ef,g^b=g^30502 conjugacy classes — view the full character table.
| maximal subgroup of | D31×#359, C2×#14520857, #16847437, … |
| maximal normal subgroup of | D31×#359, C2×#14520857, #16847437, … |
| maximal quotient of | #16843673, #16843676, #16843727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 357);