Finite Group DatabasebetaFinite Group Databasebeta| order | 10470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D349⋊C3) |
| unambiguous semidirect product | (C349⋊C3)⋊D5 |
| unambiguous semidirect product | D1745⋊C3 |
| Fitting, socle, derived, Hall | C5×C349 ⋊ C2×C3 |
| Hall | C5×C349⋊C3 ⋊ C2 |
| Hall | D1745 ⋊ C3 |
| Hall | C349⋊C3 ⋊ D5 |
| Sylow | C349 ⋊ C3×D5 |
| Sylow | C5 ⋊ D349⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C349 | C2×C3 |
| LCS | G ▷ C5×C349 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,349|c^a=c^4,d^a=d^348,d^b=d^226302 conjugacy classes — view the full character table.
| maximal subgroup of | #20296121⋊C3, #20296122⋊C3, D5×D349⋊C3, … |
| maximal normal subgroup of | #20296121⋊C3, #20296122⋊C3, D5×D349⋊C3, … |
| maximal quotient of | Dic1745⋊C3, C2×C5⋊(D349⋊C3), C5⋊(D349⋊C9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10470, 12);