Finite Group DatabasebetaFinite Group Databasebeta| order | 20956 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×D13×D31 |
| unambiguous semidirect product | (D13×C31)⋊(C2×C13) |
| unambiguous semidirect product | (C13×D31)⋊(C2×C13) |
| unambiguous semidirect product | D403⋊(C2×C13) |
| Fitting, socle, Hall | C132×C31 ⋊ C22 |
| derived | C13×C31 ⋊ C22×C13 |
| Sylow | C132 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×C13×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D13×D31 |
| commutator, cosocle, hypocenter | C13×C31 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C132×C31 | C22 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C13 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 806 |
1768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20956, 19);