Finite Group DatabasebetaFinite Group Databasebeta| order | 14770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1055 |
| unambiguous semidirect product | C5⋊(C7×D211) |
| Fitting, socle, Hall | C5×C7×C211 ⋊ C2 |
| derived, Hall | C5×C211 ⋊ C2×C7 |
| Hall | C7×C211 ⋊ D5 |
| Sylow | C211 ⋊ C7×D5 |
| Hall | C5×C7 ⋊ D211 |
| Sylow | C5 ⋊ C7×D211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1055 |
| commutator, cosocle, hypocenter | C5×C211 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C211 | C2 |
| LCS | G ▷ C5×C211 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
3703 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D5×D211, D7×D1055, D35⋊D211, … |
| maximal normal subgroup of | C7×D5×D211, D7×D1055, D35⋊D211, … |
| maximal quotient of | C7×Dic1055, C2×C7×D1055, C3×C7×D1055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14770, 9);