Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C31 ⋊ C2 |
| Sylow | C31 ⋊ #390 |
258 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^6,31|a^2=f,b^2=df,c^2=e,b^a=bd,c^a=ce,g^c=g^30328 conjugacy classes — view the full character table.
| maximal subgroup of | D31×#390, C2×#14520949, #16848170, … |
| maximal normal subgroup of | D31×#390, C2×#14520949, #16848170, … |
| maximal quotient of | Dic31⋊#95, #16843947, #16843948, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 449);