Finite Group DatabasebetaFinite Group Databasebeta| order | 31820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D37×D43 |
| unambiguous semidirect product | (C43×D37)⋊(C2×C5) |
| unambiguous semidirect product | (C37×D43)⋊(C2×C5) |
| unambiguous semidirect product | D1591⋊(C2×C5) |
| Fitting, socle, Hall | C5×C37×C43 ⋊ C22 |
| derived, Hall | C37×C43 ⋊ C22×C5 |
| Hall | C5×C43 ⋊ C2×D37 |
| Hall | C5×C37 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×C5×D37 |
| Sylow | C37 ⋊ C2×C5×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D37×D43 |
| commutator, cosocle, hypocenter | C37×C43 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C37×C43 | C22 |
| LCS | G ▷ C37×C43 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7955 |
2300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31820, 12);