Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C5×C17 ⋊ C4⋊C4 |
| Sylow | C17 ⋊ #683 |
| Sylow | C5 ⋊ #63225 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1360 |
Polycyclic presentation:
2^4,5,17|a^2=d,b^2=c,b^a=bd,e^a=e^4,f^a=f^16346 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 76);