Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| isoclinism | isoclinic class of D5×D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D5×D17 |
| unambiguous semidirect product | (D5×C17)⋊C23 |
| unambiguous semidirect product | (C5×D17)⋊C23 |
| unambiguous semidirect product | D85⋊C23 |
| Fitting, socle | C22×C5×C17 ⋊ C22 |
| derived, Hall | C5×C17 ⋊ C24 |
| Sylow | C17 ⋊ C23×D5 |
| Sylow | C5 ⋊ C23×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×D17 |
| commutator, cosocle, hypocenter | C5×C17 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C17 | C22 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C22 | |
268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 340 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 241);