Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| isoclinism | isoclinic class of #10621779 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#10621779 |
| Fitting, socle | C2×C5×C17 ⋊ C8 |
| derived, Hall | C5×C17 ⋊ C2×C8 |
| Sylow | C17 ⋊ C2×#168 |
| Sylow | C5 ⋊ C2×#3633 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10621779 |
| commutator, hypocenter | C5×C17 | C2×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C17 | C8 |
| prime radical | C2×C5×D17 | C4 |
| cosocle | C5×#595 | C22 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 170 |
52 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×#3633, C2×#13062854, C2×#13062853, … |
| maximal normal subgroup of | C2×D5×#3633, C2×#13062854, C2×#13062853 |
| maximal quotient of | D5×#10621779 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 230);