Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#69131 |
| Fitting | C2×C3×AΣL(1,𝔽16) ⋊ C2 |
| Sylow | C3 ⋊ C2×#2199 |
1392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10949249, C2×#10949250, C2×#10949241, … |
| maximal normal subgroup of | C2×#10949249, C2×#10949250, C2×#10949241, … |
| maximal quotient of | #72255121, #72255161 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323598);