Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C128 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊C128 |
| unambiguous semidirect product | (C2×C3)⋊C128 |
| derived, Sylow | C3 ⋊ C2×C128 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C64 | D3 |
| commutator, hypocenter | C3 | C2×C128 |
| Frattini | C64 | C2×D3 |
| Fitting | C2×C3×C64 | C2 |
| socle, prime radical | C22×C3 | C64 |
| cosocle | C3×C64 | C22 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C64 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 768 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 57477);