Finite Group DatabasebetaFinite Group Databasebeta| order | 1368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4296⋊Q8 |
| Hall | #4296 ⋊ Q8 |
| Hall | Dic38 ⋊ C9 |
| Sylow | C19 ⋊ Q8×C9 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 152 |
Polycyclic presentation:
2^2,3,2,3,19|a^2=d,b^2=d,c^3=e,b^a=bd,f^a=f^18,f^c=f^4,f^e=f^749 conjugacy classes — view the full character table.
| maximal subgroup of | #72241735, Q8×AGL(1,𝔽19), #72241738, … |
| maximal normal subgroup of | #72241735, Q8×AGL(1,𝔽19), #72241738, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1368, 67);