Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#2311 ⋊ C2 |
| Sylow | C3 ⋊ #11016 |
1574 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=cf,d^b=dh,f^b=fh,i^b=i^2,f^c=fh96 conjugacy classes — view the full character table.
| maximal subgroup of | #72255530, D3×#11016, #72255546 |
| maximal normal subgroup of | #72255530, D3×#11016, #72255546 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 76323);