Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#78530 |
| Fitting | C2×C3×C4×M16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3151 |
3950 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3151, D3×#78530, C2×#10784428, … |
| maximal normal subgroup of | C2×D3×#3151, C2×#10784428, C2×#10784430 |
| maximal quotient of | D3×#78530, C2×#10784428 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1039014);