Finite Group DatabasebetaFinite Group Databasebeta| order | 6410 |
| automorphism | Aut(G) order 8204800 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3205 |
| unambiguous semidirect product | C5⋊D641 |
| unambiguous semidirect product | C641⋊D5 |
| Fitting, socle, derived, Hall | C5×C641 ⋊ C2 |
| Sylow | C641 ⋊ D5 |
| Sylow | C5 ⋊ D641 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C641 | C2 |
| LCS | G ▷ C5×C641 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,641|b^a=b^4,c^a=c^6401604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27165537, #27165538, D5×D641, … |
| maximal normal subgroup of | #27165537, #27165538, D5×D641, … |
| maximal quotient of | Dic3205, C2×D3205, C3×D3205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6410, 5);