Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C3×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ #24398 |
1476 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^2,c^b=cg,g^b=gh,f^c=fh,g^c=gh87 conjugacy classes — view the full character table.
| maximal subgroup of | #72270318, D3×#24398, #72270461 |
| maximal normal subgroup of | #72270318, D3×#24398, #72270461 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 206835);