Finite Group DatabasebetaFinite Group Databasebeta| order | 10570 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D151⋊C5 |
| unambiguous semidirect product | D151⋊(C5×C7) |
| unambiguous semidirect product | (C151⋊C5)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D151)⋊C5 |
| Fitting, socle, Hall | C7×C151 ⋊ C2×C5 |
| derived, Sylow | C151 ⋊ C2×C5×C7 |
| Hall | C7×C151⋊C5 ⋊ C2 |
| Hall | C7×D151 ⋊ C5 |
| Hall | C151⋊C5 ⋊ C2×C7 |
| Hall | D151 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D151⋊C5 |
| commutator, cosocle, hypocenter | C151 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C151 | C2×C5 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
175 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D151⋊C5, C2×C7×D151⋊C5, C3×C7×D151⋊C5, … |
| maximal normal subgroup of | D7×D151⋊C5, C2×C7×D151⋊C5, C3×C7×D151⋊C5, … |
| maximal quotient of | C7×Dic151⋊C5, C2×C7×D151⋊C5, C3×C7×D151⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10570, 10);