Finite Group DatabasebetaFinite Group Databasebeta| order | 8450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C13 |
| direct product | C5×C5⋊(C13⋊D13) |
| unambiguous semidirect product | C5⋊(C5×C13⋊D13) |
| unambiguous semidirect product | C13⋊(C5×D65) |
| Fitting, socle, Hall | C52×C132 ⋊ C2 |
| derived | C5×C132 ⋊ C2×C5 |
| Sylow | C132 ⋊ C5×D5 |
| Sylow | C52 ⋊ C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C5⋊(C13⋊D13) |
| commutator, hypocenter | C5×C132 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C132 | C2 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C5 | |
160 conjugacy classes of subgroups.
2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8450, 22);