Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C31 ⋊ #397 |
170 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 59 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=e,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^30322 conjugacy classes — view the full character table.
| maximal subgroup of | #16843710, #16843712, #16844697, … |
| maximal normal subgroup of | #16843710, #16843712, #16844697, … |
| maximal quotient of | #16843956, #16843958, #16843967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 474);