Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C31 ⋊ C2 |
| Sylow | C31 ⋊ #518 |
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^6,31|a^2=f,b^a=be,d^a=de,c^b=ce,g^c=g^30334 conjugacy classes — view the full character table.
| maximal subgroup of | #16845818, #16845990, #16845993, … |
| maximal normal subgroup of | #16845818, #16845990, #16845993, … |
| maximal quotient of | #16848063, #16848064, #16848066, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 1022);