Finite Group DatabasebetaFinite Group Databasebeta| order | 10770 |
| automorphism | Aut(G) order 15422640 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5385 |
| unambiguous semidirect product | C3⋊D1795 |
| unambiguous semidirect product | C5⋊D1077 |
| unambiguous semidirect product | C359⋊D15 |
| Fitting, socle, derived, Hall | C3×C5×C359 ⋊ C2 |
| Hall | C5×C359 ⋊ D3 |
| Hall | C3×C359 ⋊ D5 |
| Sylow | C359 ⋊ D15 |
| Hall | C3×C5 ⋊ D359 |
| Sylow | C5 ⋊ D1077 |
| Sylow | C3 ⋊ D1795 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C359 | C2 |
| LCS | G ▷ C3×C5×C359 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,359|b^a=b^2,c^a=c^4,d^a=d^3582694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D15×D359, D5×D1077, D3×D1795, … |
| maximal normal subgroup of | D15×D359, D5×D1077, D3×D1795, … |
| maximal quotient of | Dic5385, C2×D5385, D16155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10770, 8);