Finite Group DatabasebetaFinite Group Databasebeta| order | 10150 |
| isoclinism | isoclinic class of D175 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D175 |
| unambiguous semidirect product | C7⋊(C29×D25) |
| unambiguous semidirect product | C25⋊(D7×C29) |
| Fitting, Hall | C7×C25×C29 ⋊ C2 |
| derived, Hall | C7×C25 ⋊ C2×C29 |
| Hall | C25×C29 ⋊ D7 |
| Hall | C7×C29 ⋊ D25 |
| Sylow | C25 ⋊ D7×C29 |
| Sylow | C7 ⋊ C29×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D175 |
| commutator, cosocle, hypocenter | C7×C25 | C2×C29 |
| Frattini | C5 | C29×D35 |
| Fitting | C7×C25×C29 | C2 |
| socle | C5×C7×C29 | D5 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 ◁ C29 | |
24 conjugacy classes of subgroups.
2581 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×D175, D7×C29×D25, D175⋊D29, … |
| maximal normal subgroup of | D29×D175, D7×C29×D25, D175⋊D29, … |
| maximal quotient of | C29×Dic175, C2×C29×D175, C3×C29×D175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10150, 8);