Finite Group DatabasebetaFinite Group Databasebeta| order | 31820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×Dic185 |
| derived, Hall | C5×C37 ⋊ C4×C43 |
| Hall | C5×C37×C43 ⋊ C4 |
| Hall | C37×C43 ⋊ Dic5 |
| Hall | C5×C43 ⋊ Dic37 |
| Sylow | C37 ⋊ Dic5×C43 |
| Sylow | C5 ⋊ C43×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | D185 |
| commutator, hypocenter | C5×C37 | C4×C43 |
| Frattini | C2 | C43×D185 |
| Fitting, socle, prime radical | C2×C5×C37×C43 | C2 |
| cosocle | C2×C5×C37 | C2×C43 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C2×C43 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31820 |
8084 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31820, 7);