Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting, Sylow | #62989 ⋊ C3 |
1283 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 1283 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
Polycyclic presentation:
3,2^8|b^2=hi,c^2=h,b^a=beg,d^a=dfhi,e^a=egi,f^a=di,g^a=e,c^b=ch,d^b=di,g^d=gi,f^e=fi55 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085179);