Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#3540 ⋊ C2 |
| Sylow | C3 ⋊ #33555 |
1146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|c^2=h,d^2=h,b^a=be,c^a=cf,g^a=gh,i^a=i^2,d^b=dh,f^b=fgh,e^c=eg,f^e=fh72 conjugacy classes — view the full character table.
| maximal subgroup of | #72247954, D3×#33555, #72247965 |
| maximal normal subgroup of | #72247954, D3×#33555, #72247965 |
| maximal quotient of | #72254519 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323667);