Finite Group DatabasebetaFinite Group Databasebeta| order | 33054 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D2361 |
| unambiguous semidirect product | C3⋊(C7×D787) |
| unambiguous semidirect product | C787⋊(D3×C7) |
| Fitting, socle, Hall | C3×C7×C787 ⋊ C2 |
| derived, Hall | C3×C787 ⋊ C2×C7 |
| Hall | C7×C787 ⋊ D3 |
| Sylow | C787 ⋊ D3×C7 |
| Hall | C3×C7 ⋊ D787 |
| Sylow | C3 ⋊ C7×D787 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D2361 |
| commutator, cosocle, hypocenter | C3×C787 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C787 | C2 |
| LCS | G ▷ C3×C787 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16527 |
8274 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33054, 10);