Finite Group DatabasebetaFinite Group Databasebeta| order | 1040 |
| isoclinism | isoclinic class of #63122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#10587066 |
| derived, Hall | C5×C13 ⋊ C2×C8 |
| Sylow | C13 ⋊ C2×#170 |
| Sylow | C5 ⋊ C2×#1057 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #63122 |
| commutator, hypocenter | C5×C13 | C2×C8 |
| Frattini | C2 | C2×#63122 |
| Fitting, socle, prime radical | C22×C5×C13 | C4 |
| cosocle | Dic65 | C22 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C22 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1040 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1040, 131);