Finite Group DatabasebetaFinite Group Databasebeta| order | 37820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C31⋊#6923 |
| Fitting, socle, Hall | C5×C31×C61 ⋊ C4 |
| derived, Hall | C31×C61 ⋊ C4×C5 |
| Hall | C5×C61 ⋊ Dic31 |
| Hall | C5×C31 ⋊ #6923 |
| Sylow | C61 ⋊ C5×Dic31 |
| Sylow | C31 ⋊ C5×#6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C31⋊#6923 |
| commutator, hypocenter | C31×C61 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C31×C61 | C4 |
| prime radical | C5×C31×D61 | C2 |
| cosocle | C31×D61 | C2×C5 |
| LCS | G ▷ C31×C61 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9455 |
2495 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37820, 77);