Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#2121 ⋊ C2 |
| Sylow | C3 ⋊ #33551 |
1326 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|b^a=be,c^a=cf,g^a=gh,i^a=i^2,d^b=dh,f^b=fgh,e^c=eg,i^c=i^2,f^e=fh57 conjugacy classes — view the full character table.
| maximal subgroup of | #72219819, #72231720, #72248278, … |
| maximal normal subgroup of | D3×#33551, #72219819, #72231720, … |
| maximal quotient of | C2×#10949249, #72248436, #72248456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323630);