Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#447 ⋊ C2 |
| Sylow | C3 ⋊ #9914 |
1356 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fh,c^b=cf,d^b=dg,d^c=dh,i^c=i^278 conjugacy classes — view the full character table.
| maximal subgroup of | #72247804, D3×#9914, #72255463 |
| maximal normal subgroup of | #72247804, D3×#9914, #72255463 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 69761);