Finite Group DatabasebetaFinite Group Databasebeta| order | 33780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊D563 |
| unambiguous semidirect product | D1689⋊D5 |
| unambiguous semidirect product | D2815⋊D3 |
| Fitting, socle, derived, Hall | C3×C5×C563 ⋊ C22 |
| Hall | C5×C563 ⋊ C2×D3 |
| Hall | C3×C563 ⋊ C2×D5 |
| Sylow | C563 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×D563 |
| Sylow | C5 ⋊ D3×D563 |
| Sylow | C3 ⋊ D5×D563 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C563 | C22 |
| LCS | G ▷ C3×C5×C563 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8445 |
Polycyclic presentation:
2^2,3,5,563|d^a=d^4,e^a=e^562,c^b=c^2,d^b=d^42541 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33780, 20);