Finite Group DatabasebetaFinite Group Databasebeta| order | 17739 |
| isoclinism | isoclinic class of C73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C81 · Schur multiplier (H2) = C3 |
| direct product | C81×C73⋊C3 |
| Fitting | C73×C81 ⋊ C3 |
| derived, Sylow | C73 ⋊ C3×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C81 | C73⋊C3 |
| commutator, hypocenter | C73 | C3×C81 |
| Frattini | C27 | C3×C73⋊C3 |
| Fitting | C73×C81 | C3 |
| socle | C3×C73 | C3×C27 |
| prime radical | C3×C73⋊C3 | C27 |
| cosocle | C27×C73 | C32 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C81 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5913 |
2187 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17739, 124);