Finite Group DatabasebetaFinite Group Databasebeta| order | 15050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊(D43⋊C7) |
| unambiguous semidirect product | (C43⋊C7)⋊D25 |
| unambiguous semidirect product | D1075⋊C7 |
| Fitting, derived, Hall | C25×C43 ⋊ C2×C7 |
| Hall | C25×C43⋊C7 ⋊ C2 |
| Hall | D1075 ⋊ C7 |
| Hall | C43⋊C7 ⋊ D25 |
| Sylow | C43 ⋊ C7×D25 |
| Sylow | C25 ⋊ D43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C25×C43 | C2×C7 |
| Frattini | C5 | C5⋊(D43⋊C7) |
| socle | C5×C43 | C7×D5 |
| LCS | G ▷ C25×C43 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1075 |
Polycyclic presentation:
2,5,7,43,5|b^5=e^4,b^a=b^4e,d^a=d^42,e^a=e^4,d^c=d^41173 conjugacy classes — view the full character table.
| maximal subgroup of | D25×D43⋊C7, C2×C25⋊(D43⋊C7) |
| maximal normal subgroup of | D25×D43⋊C7, C2×C25⋊(D43⋊C7) |
| maximal quotient of | (C43⋊C7)⋊Dic25, C2×C25⋊(D43⋊C7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15050, 12);