Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C281 ⋊ #330 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17984 |
Polycyclic presentation:
2^6,281|a^2=d,b^2=e,c^2=f,d^2=e,b^a=bc,c^a=ce,g^a=g^280,c^b=cf,d^b=def1979 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #330×D281, C2×#31823205, #49093890, … |
| maximal normal subgroup of | #330×D281, C2×#31823205, #49093890, … |
| maximal quotient of | #49093126, #49093184, C2×#31823205 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 291);