Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #10960 |
1526 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,c^2=ef,b^a=bd,c^a=ce,d^a=dh,e^a=eh,g^a=gh,i^a=i^2,d^b=dh,e^b=eh,f^b=fh,d^c=dh,e^c=eh,f^c=fh144 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10960, #72258850 |
| maximal normal subgroup of | D3×#10960, #72258850 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 76035);