Finite Group DatabasebetaFinite Group Databasebeta| order | 20770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2077 |
| unambiguous semidirect product | C67⋊(C5×D31) |
| Fitting, socle, Hall | C5×C31×C67 ⋊ C2 |
| derived, Hall | C31×C67 ⋊ C2×C5 |
| Hall | C5×C67 ⋊ D31 |
| Hall | C5×C31 ⋊ D67 |
| Sylow | C67 ⋊ C5×D31 |
| Sylow | C31 ⋊ C5×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2077 |
| commutator, cosocle, hypocenter | C31×C67 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C31×C67 | C2 |
| LCS | G ▷ C31×C67 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10385 |
5200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20770, 5);