Finite Group DatabasebetaFinite Group Databasebeta| order | 1860 |
| isoclinism | isoclinic class of AGL(1,𝔽31) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C31 ⋊ C2×C3×C5 |
| derived, Sylow | C31 ⋊ C22×C3×C5 |
| Hall | C2×D31⋊C5 ⋊ C3 |
| Hall | (C31⋊C3)⋊C5 ⋊ C22 |
| Hall | C2×D31⋊C3 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C22×C3 |
| Hall | C2×D31 ⋊ C3×C5 |
| Hall | C31⋊C3 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽31) |
| commutator, cosocle, hypocenter | C31 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31 | C2×C3×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 62 |
62 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1860, 20);