Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C221 |
| direct product | C26×Dic3 |
| derived, Sylow | C3 ⋊ C26×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | D3 |
| commutator, hypocenter | C3 | C26×C4 |
| Frattini | C2 | C26×D3 |
| Fitting, socle, prime radical | C27×C3 | C2 |
| cosocle | C2×C3 | C27 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C27 | |
111198 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, 1083443);