Finite Group DatabasebetaFinite Group Databasebeta| order | 870 |
| isoclinism | isoclinic class of D87 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D87 |
| unambiguous semidirect product | C3⋊(C5×D29) |
| unambiguous semidirect product | C29⋊(C5×D3) |
| Fitting, socle, Hall | C3×C5×C29 ⋊ C2 |
| derived, Hall | C3×C29 ⋊ C2×C5 |
| Hall | C5×C29 ⋊ D3 |
| Sylow | C29 ⋊ C5×D3 |
| Hall | C3×C5 ⋊ D29 |
| Sylow | C3 ⋊ C5×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D87 |
| commutator, cosocle, hypocenter | C3×C29 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C29 | C2 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 435 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×D29, D5×D87, D15⋊D29, … |
| maximal normal subgroup of | C5×D3×D29, D5×D87, D15⋊D29, … |
| maximal quotient of | C5×Dic87, C2×C5×D87, C5×D261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(870, 5);