Finite Group DatabasebetaFinite Group Databasebeta| order | 10850 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7×C31 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×D5×C31 |
| unambiguous semidirect product | C5⋊(C2×C5×C7×C31) |
| Fitting, socle, Hall | C52×C7×C31 ⋊ C2 |
| derived | C5 ⋊ C2×C5×C7×C31 |
| Hall | C52×C31 ⋊ C2×C7 |
| Hall | C52×C7 ⋊ C2×C31 |
| Sylow | C52 ⋊ C2×C7×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7×C31 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C5×C7×C31 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C31 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C5×C7×C31 | |
40 conjugacy classes of subgroups.
4340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D5×D31, C5×D5×D7×C31, C5×D5×D217, … |
| maximal normal subgroup of | C5×C7×D5×D31, C5×D5×D7×C31, C5×D5×D217, … |
| maximal quotient of | C5×C7×Dic5×C31, C2×C5×C7×D5×C31, C3×C5×C7×D5×C31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10850, 29);