Finite Group DatabasebetaFinite Group Databasebeta| order | 37820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31×C61 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×C31×C61 |
| Fitting, socle, Hall | C5×C31×C61 ⋊ C4 |
| derived, Sylow | C5 ⋊ C4×C31×C61 |
| Hall | C5×C61 ⋊ C4×C31 |
| Hall | C5×C31 ⋊ C4×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31×C61 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C31×C61 |
| Frattini | C1 | G |
| Fitting, socle | C5×C31×C61 | C4 |
| prime radical | D5×C31×C61 | C2 |
| cosocle | D5 | C2×C31×C61 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C31×C61 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9455 |
9455 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37820, 79);