Finite Group DatabasebetaFinite Group Databasebeta| order | 1950 |
| isoclinism | isoclinic class of C5⋊(D13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C52×C13 ⋊ C2×C3 |
| derived | C5×C13 ⋊ C2×C3×C5 |
| Hall | C52×C13⋊C3 ⋊ C2 |
| Hall | C5×D65 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C5×D5 |
| Sylow | C52 ⋊ D13⋊C3 |
| Sylow | C13 ⋊ C3×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C5⋊(D13⋊C3) |
| commutator, cosocle, hypocenter | C5×C13 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13 | C2×C3 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 130 |
110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1950, 17);