Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#3058 ⋊ C2 |
| Sylow | C3 ⋊ #33531 |
1122 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1122 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|e^2=gh,g^2=h,b^a=be,c^a=cf,e^a=eg,g^a=gh,e^b=eg,f^b=fh,g^b=gh,i^b=i^2,d^c=dh,e^c=eh72 conjugacy classes — view the full character table.
| maximal subgroup of | #72270193, #72270232, #72270233, … |
| maximal normal subgroup of | #72270193, #72270232, #72270233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323470);