Finite Group DatabasebetaFinite Group Databasebeta| order | 10870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1087 |
| unambiguous semidirect product | C1087⋊(C2×C5) |
| Fitting, socle, Hall | C5×C1087 ⋊ C2 |
| derived, Sylow | C1087 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1087 |
| commutator, cosocle, hypocenter | C1087 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C1087 | C2 |
| LCS | G ▷ C1087 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
2725 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1087, C2×C5×D1087, C3×C5×D1087, … |
| maximal normal subgroup of | D5×D1087, C2×C5×D1087, C3×C5×D1087, … |
| maximal quotient of | C5×Dic1087, C2×C5×D1087, C3×C5×D1087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10870, 2);