Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C7×M16 ⋊ C22 |
| Hall | C3×C7 ⋊ C2×#104 |
| Sylow | C7 ⋊ D3×#104 |
| Sylow | C3 ⋊ D7×#104 |
340 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^6,3,7|c^2=d,d^2=f,e^2=f,c^a=ce,e^a=ef,h^a=h^6,c^b=ce,e^b=ef,g^b=g^2,e^c=ef114 conjugacy classes — view the full character table.
| maximal subgroup of | #72244315, #72244338, D3×D7×#104, … |
| maximal normal subgroup of | #72244315, #72244338, D3×D7×#104, … |
| maximal quotient of | #72246681 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 2904);