Finite Group DatabasebetaFinite Group Databasebeta| order | 6460 |
| automorphism | Aut(G) order 3720960 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3230 |
| direct product | C2×D1615 |
| unambiguous semidirect product | (C2×C5)⋊D323 |
| unambiguous semidirect product | (C2×C17)⋊D95 |
| unambiguous semidirect product | (C2×C19)⋊D85 |
| Fitting, socle | C2×C5×C17×C19 ⋊ C2 |
| derived, Hall | C5×C17×C19 ⋊ C22 |
| Hall | C17×C19 ⋊ C2×D5 |
| Hall | C5×C19 ⋊ C2×D17 |
| Hall | C5×C17 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D85 |
| Sylow | C17 ⋊ C2×D95 |
| Sylow | C5 ⋊ C2×D323 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1615 |
| commutator, hypocenter | C5×C17×C19 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C17×C19 | C2 |
| LCS | G ▷ C5×C17×C19 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
1618 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5⋊(C17⋊(D19⋊C3)), D3×D1615, C2×D4845, … |
| maximal normal subgroup of | C2×C5⋊(C17⋊(D19⋊C3)), C2×C3×D1615, C2×C5×D1615, … |
| maximal quotient of | D3×D1615, C2×D4845, C2×C3×D1615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6460, 29);