Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C3×#1879 ⋊ 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,i^a=i^2,d^b=dh,e^b=eh,i^c=i^2,i^d=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#21452, #72269876, #72269936, … |
| maximal normal subgroup of | D3×#21452, #72269876, #72269936, … |
| maximal quotient of | #72219837, #72270157, #72270214 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 175214);