Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| isoclinism | isoclinic class of #89167 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#89170 |
| Hall | C5×C11 ⋊ C22×Q8 |
| Sylow | C11 ⋊ C22×Dic10 |
| Sylow | C5 ⋊ C22×Dic22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D5×D11 |
| commutator, cosocle | C2×C5×C11 | C24 |
| Frattini | C2 | C22×D5×D11 |
| Fitting, socle, prime radical | C23×C5×C11 | C22 |
| hypocenter | C5×C11 | C22×Q8 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C23 | |
312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1760 |
212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1214);