Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#1910 ⋊ C2 |
| Sylow | C3 ⋊ #23990 |
1260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|b^2=e,g^2=h,b^a=be,c^a=cf,d^a=de,g^a=gh,i^a=i^2,c^b=cg,i^b=i^2,e^c=eh,g^c=gh,i^c=i^2,f^d=fh69 conjugacy classes — view the full character table.
| maximal subgroup of | #72258014, #72258048, D3×#23990 |
| maximal normal subgroup of | #72258014, #72258048, D3×#23990 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 202074);