Finite Group DatabasebetaFinite Group Databasebeta| order | 10850 |
| isoclinism | isoclinic class of D217 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D217 |
| unambiguous semidirect product | C7⋊(C52×D31) |
| Fitting, socle, Hall | C52×C7×C31 ⋊ C2 |
| derived, Hall | C7×C31 ⋊ C2×C52 |
| Hall | C52×C31 ⋊ D7 |
| Hall | C52×C7 ⋊ D31 |
| Sylow | C31 ⋊ C52×D7 |
| Sylow | C7 ⋊ C52×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D217 |
| commutator, cosocle, hypocenter | C7×C31 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C31 | C2 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C52 | |
64 conjugacy classes of subgroups.
2750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D7×D31, C5×D5×D217, C5×D35⋊D31, … |
| maximal normal subgroup of | C52×D7×D31, C5×D5×D217, C5×D35⋊D31, … |
| maximal quotient of | C52×Dic217, C2×C52×D217, C3×C52×D217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10850, 30);