Finite Group DatabasebetaFinite Group Databasebeta| order | 19780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C43 · Schur multiplier (H2) = C2 |
| direct product | C2×C43×D115 |
| unambiguous semidirect product | (C2×C5)⋊(C43×D23) |
| unambiguous semidirect product | (C2×C23)⋊(D5×C43) |
| Fitting, socle | C2×C5×C23×C43 ⋊ C2 |
| derived, Hall | C5×C23 ⋊ C22×C43 |
| Hall | C5×C23×C43 ⋊ C22 |
| Hall | C23×C43 ⋊ C2×D5 |
| Hall | C5×C43 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D5×C43 |
| Sylow | C5 ⋊ C2×C43×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | D115 |
| commutator, cosocle, hypocenter | C5×C23 | C22×C43 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C23×C43 | C2 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C2×C43 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9890 |
5074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19780, 22);