Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M16×C281 ⋊ C2 |
| Sylow | C281 ⋊ #408 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8992 |
Polycyclic presentation:
2^6,281|a^2=e,e^2=f,b^a=bd,g^a=g^280,c^b=cf,g^b=g^2802828 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49093240, #49095252, #49095265, … |
| maximal normal subgroup of | #49093240, #49095252, #49095265, … |
| maximal quotient of | #49093652, #49093656, #49093660, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 517);