Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×C8×D17 |
| Fitting | C5×C8×C17 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C5×C8 |
| Hall | C5×C17 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C8 | D17 |
| commutator, hypocenter | C17 | C2×C5×C8 |
| Frattini | C4 | C2×C5×D17 |
| Fitting | C5×C8×C17 | C2 |
| socle | C2×C5×C17 | C2×C4 |
| prime radical | C2×C5×D17 | C4 |
| cosocle | C4×C17 | C22×C5 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C5×C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 680 |
400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 36);