Finite Group DatabasebetaFinite Group Databasebeta| order | 10570 |
| automorphism | Aut(G) order 19026000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5285 |
| unambiguous semidirect product | C5⋊D1057 |
| unambiguous semidirect product | C7⋊D755 |
| unambiguous semidirect product | C151⋊D35 |
| Fitting, socle, derived, Hall | C5×C7×C151 ⋊ C2 |
| Hall | C7×C151 ⋊ D5 |
| Hall | C5×C151 ⋊ D7 |
| Sylow | C151 ⋊ D35 |
| Hall | C5×C7 ⋊ D151 |
| Sylow | C7 ⋊ D755 |
| Sylow | C5 ⋊ D1057 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C151 | C2 |
| LCS | G ▷ C5×C7×C151 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,151|b^a=b^4,c^a=c^6,d^a=d^1502644 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D35×D151, D7×D755, D5×D1057, … |
| maximal normal subgroup of | D35×D151, D7×D755, D5×D1057, … |
| maximal quotient of | Dic5285, C2×D5285, C3×D5285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10570, 9);