Finite Group DatabasebetaFinite Group Databasebeta| order | 17270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1727 |
| unambiguous semidirect product | C157⋊(C5×D11) |
| Fitting, socle, Hall | C5×C11×C157 ⋊ C2 |
| derived, Hall | C11×C157 ⋊ C2×C5 |
| Hall | C5×C157 ⋊ D11 |
| Sylow | C157 ⋊ C5×D11 |
| Hall | C5×C11 ⋊ D157 |
| Sylow | C11 ⋊ C5×D157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1727 |
| commutator, cosocle, hypocenter | C11×C157 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C157 | C2 |
| LCS | G ▷ C11×C157 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8635 |
4325 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D11×D157, D5×D1727, D55⋊D157, … |
| maximal normal subgroup of | C5×D11×D157, D5×D1727, D55⋊D157, … |
| maximal quotient of | C5×Dic1727, C2×C5×D1727 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17270, 5);