Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#543 ⋊ C2 |
| Sylow | C3 ⋊ #18318 |
1172 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1172 conjugacy classes of subgroups — too many to draw. Only its 183 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|b^2=g,e^2=g,b^a=be,c^a=cf,d^a=dgh,e^a=eg,i^a=i^2,e^b=eg,f^b=fh,e^c=eh81 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 143688);