Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×#1819 ⋊ C2 |
| Sylow | C3 ⋊ #29635 |
1596 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1596 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|c^2=h,b^a=be,c^a=cf,g^a=gh,i^a=i^2,c^b=cg,f^b=fh,i^b=i^2,d^c=de,i^c=i^269 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 275283);