Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C7⋊S4)⋊Q8 |
| Sylow | C7 ⋊ Q8×S4 |
312 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 43 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:
2^4,3,7,2^2|a^2=d,b^2=d,c^2=d,c^a=cd,f^a=f^6,c^b=cd,e^b=e^2,g^b=gh,g^e=h,h^e=gh67 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11319);