Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#2626 ⋊ C2 |
| Sylow | C3 ⋊ #9922 |
1278 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fh,c^b=cf,d^b=dg,i^b=i^2,d^c=dh72 conjugacy classes — view the full character table.
| maximal subgroup of | #72255458, D3×#9922, #72255493 |
| maximal normal subgroup of | #72255458, D3×#9922, #72255493 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 69818);