Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C281 ⋊ #357 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8992 |
Polycyclic presentation:
2^6,281|a^2=d,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^280,c^b=ce,e^b=ef1982 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #357×D281, C2×#31823264, #49097007, … |
| maximal normal subgroup of | #357×D281, C2×#31823264, #49097007, … |
| maximal quotient of | #49093264, #49093312, #49093349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 350);