Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×C42×D4 ⋊ C2 |
| Sylow | C3 ⋊ #21503 |
1260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=e,d^2=g,f^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^2,d^c=dh,f^c=fh144 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#21503 |
| maximal normal subgroup of | D3×#21503 |
| maximal quotient of | #72226026 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 175818);