Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #10621175 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, Hall | C7×#383 ⋊ C3 |
| derived | C42×C7 ⋊ C3×C4 |
| Sylow | #383 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ #383⋊C3 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2,3,2^3,7,2^2|a^2=c,d^2=g,e^2=gh,d^a=dh,e^a=eg,d^b=de,e^b=dgh,f^b=f^2,g^b=h,h^b=gh76 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4353);