Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | #90503 ⋊ C3 |
| Sylow | C7 ⋊ #519⋊C3 |
172 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^2,3,2^3,7,2|a^2=d,e^2=h,f^2=h,b^a=bh,g^a=g^6,e^c=ef,f^c=e,g^c=g^2,f^e=fh58 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6961);