Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#2199 ⋊ 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,d^b=dh,f^b=fgh,e^c=eg,i^c=i^2,i^d=i^2,f^e=fh51 conjugacy classes — view the full character table.
| maximal subgroup of | #72215235, #72233239, C2×#10949243, … |
| maximal normal subgroup of | D3×#33551, C2×#10949243, #72255218, … |
| maximal quotient of | #72248434, #72248498, C2×#10949243, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323624);