Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#1889 ⋊ C2 |
| Sylow | C3 ⋊ #33020 |
1824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|c^2=e,b^a=be,c^a=cf,d^a=dg,i^b=i^2,g^c=gh,f^d=fh81 conjugacy classes — view the full character table.
| maximal subgroup of | #72248888, D3×#33020, #72248912, … |
| maximal normal subgroup of | #72248888, D3×#33020, #72248912, … |
| maximal quotient of | #72270608 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 319443);