Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Hall | C3×C7 ⋊ #578 |
| Sylow | C7 ⋊ #5779 |
| Sylow | C3 ⋊ #90470 |
496 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^6,3,7|c^2=f,e^2=f,b^a=bf,d^a=df,h^a=h^6,d^b=df,g^b=g^2,d^c=de,e^c=ef,e^d=ef87 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 8603);