Finite Group DatabasebetaFinite Group Databasebeta| order | 15050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D301 |
| unambiguous semidirect product | C7⋊(C25×D43) |
| unambiguous semidirect product | C43⋊(D7×C25) |
| Fitting, Hall | C7×C25×C43 ⋊ C2 |
| derived, Hall | C7×C43 ⋊ C2×C25 |
| Hall | C25×C43 ⋊ D7 |
| Hall | C7×C25 ⋊ D43 |
| Sylow | C43 ⋊ D7×C25 |
| Sylow | C7 ⋊ C25×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D301 |
| commutator, hypocenter | C7×C43 | C2×C25 |
| Frattini | C5 | C5×D301 |
| Fitting | C7×C25×C43 | C2 |
| socle, cosocle | C5×C7×C43 | C2×C5 |
| prime radical | C5×D301 | C5 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7525 |
3800 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C25×D43, D25×D301, D175⋊D43, … |
| maximal normal subgroup of | D7×C25×D43, D25×D301, D175⋊D43, … |
| maximal quotient of | C25×Dic301, C2×C25×D301 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15050, 5);