Finite Group DatabasebetaFinite Group Databasebeta| order | 1368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(#4294⋊C2) |
| Hall | #4294 ⋊ D4 |
| Hall | D76 ⋊ C9 |
| Sylow | C19 ⋊ D4×C9 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 684 |
Polycyclic presentation:
2^2,3,2,3,19|b^2=d,c^3=e,b^a=bd,f^a=f^18,f^c=f^1181 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1368, 9);