Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | C7×SL(2,𝔽3) ⋊ C2×C4 |
| Sylow | C7 ⋊ #5426 |
158 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^3,3,7,2^3|a^2=c,b^2=h,f^2=h,g^2=h,b^a=bh,d^a=d^2,e^a=e^6,f^a=fg,g^a=gh,f^d=g,g^d=fgh,g^f=gh110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6483);