Finite Group DatabasebetaFinite Group Databasebeta| order | 10410 |
| automorphism | Aut(G) order 14407440 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5205 |
| unambiguous semidirect product | C3⋊D1735 |
| unambiguous semidirect product | C5⋊D1041 |
| unambiguous semidirect product | C347⋊D15 |
| Fitting, socle, derived, Hall | C3×C5×C347 ⋊ C2 |
| Hall | C5×C347 ⋊ D3 |
| Hall | C3×C347 ⋊ D5 |
| Sylow | C347 ⋊ D15 |
| Hall | C3×C5 ⋊ D347 |
| Sylow | C5 ⋊ D1041 |
| Sylow | C3 ⋊ D1735 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C347 | C2 |
| LCS | G ▷ C3×C5×C347 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,347|b^a=b^2,c^a=c^4,d^a=d^3462604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D15×D347, D5×D1041, D3×D1735, … |
| maximal normal subgroup of | D15×D347, D5×D1041, D3×D1735, … |
| maximal quotient of | Dic5205, C2×D5205, D15615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10410, 8);