Finite Group DatabasebetaFinite Group Databasebeta| order | 20970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D3495 |
| unambiguous semidirect product | C5⋊(C3⋊D699) |
| unambiguous semidirect product | C233⋊(C3⋊D15) |
| Fitting, socle, derived, Hall | C32×C5×C233 ⋊ C2 |
| Hall | C32×C233 ⋊ D5 |
| Hall | C5×C233 ⋊ C3⋊D3 |
| Sylow | C233 ⋊ C3⋊D15 |
| Hall | C32×C5 ⋊ D233 |
| Sylow | C32 ⋊ D1165 |
| Sylow | C5 ⋊ C3⋊D699 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C233 | C2 |
| LCS | G ▷ C32×C5×C233 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10485 |
Polycyclic presentation:
2,3^2,5,233|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^2325244 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20970, 20);