Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×C4×M32 ⋊ C2 |
| Sylow | C3 ⋊ #13210 |
510 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=dfg,c^2=e,d^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^2,d^b=dh,f^b=fh132 conjugacy classes — view the full character table.
| maximal subgroup of | #72225882, #72225885, #72225887, … |
| maximal normal subgroup of | #72225882, #72225885, #72225887, … |
| maximal quotient of | #72225885, #72226126 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 87816);