Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C3 ⋊ #23446 |
1994 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|b^2=h,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,d^b=dh,i^b=i^2,e^c=eh90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 196830);