Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C3×#2943 ⋊ C2 |
| Sylow | C3 ⋊ C4×#575 |
2842 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,c^2=g,e^2=h,f^2=h,b^a=bf,d^a=dh,f^a=fh,f^b=fh,i^c=i^2,i^d=i^2132 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#575 |
| maximal normal subgroup of | C4×D3×#575 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033651);