Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C31×M32 ⋊ C2 |
| Sylow | C31 ⋊ #361 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^6,31|a^2=d,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^30,c^b=cef,d^b=df,e^b=ef,g^b=g^30316 conjugacy classes — view the full character table.
| maximal subgroup of | D31×#361, C2×#14520863, #16847459, … |
| maximal normal subgroup of | D31×#361, C2×#14520863, #16847459, … |
| maximal quotient of | #16843679, #16843727, #16843758, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 363);