Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C22×C5×#595 |
| unambiguous semidirect product | D17⋊(C2×C4×C5) |
| Fitting, socle | C22×C5×C17 ⋊ C4 |
| derived, Sylow | C17 ⋊ C22×C4×C5 |
| Hall | C5×C17 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | #595 |
| commutator, hypocenter | C17 | C22×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C17 | C4 |
| prime radical | C22×C5×D17 | C2 |
| cosocle | D17 | C23×C5 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22×C5 | |
108 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, 235);