Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C31 ⋊ C2 |
| Sylow | C31 ⋊ #551 |
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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=e,b^2=f,b^a=be,c^a=cf,d^b=de,g^b=g^30325 conjugacy classes — view the full character table.
| maximal subgroup of | D31×#551, C2×#14521725, #16859262, … |
| maximal normal subgroup of | D31×#551, C2×#14521725, #16859262, … |
| maximal quotient of | #16848556, #16848560, #16848565, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 1225);