Finite Group DatabasebetaFinite Group Databasebeta| order | 37820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×#34038660 |
| Fitting, socle | C2×C31×C61 ⋊ C2×C5 |
| derived, Hall | C31×C61 ⋊ C22×C5 |
| Hall | #22628159 ⋊ C22 |
| Hall | C2×C31×D61 ⋊ C5 |
| Hall | C2×D61 ⋊ ΓL(1,𝔽32) |
| Sylow | C61 ⋊ C22×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C2×D61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #34038660 |
| commutator, cosocle, hypocenter | C31×C61 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C61 | C2×C5 |
| LCS | G ▷ C31×C61 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3782 |
416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37820, 64);