Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C3×C4×#121 ⋊ C2 |
| Sylow | C3 ⋊ #21452 |
1952 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,d^2=g,e^2=h,b^a=be,c^a=cf,e^a=eh,d^b=dh,e^b=eh,i^b=i^2120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#21452, #72269976, #72270054 |
| maximal normal subgroup of | D3×#21452, #72269976, #72270054 |
| maximal quotient of | #72219845, #72270203 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 175209);