Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #108×C281 ⋊ C2 |
| Sylow | C281 ⋊ #444 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4496 |
Polycyclic presentation:
2^6,281|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^b=g^280,g^c=g^2801982 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49097193, #49097197, #49097200, … |
| maximal normal subgroup of | #49097193, #49097197, #49097200, … |
| maximal quotient of | #49094114, #49094121, #49094126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 670);