Finite Group DatabasebetaFinite Group Databasebeta| order | 10950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊(D73⋊C3) |
| unambiguous semidirect product | (C73⋊C3)⋊D25 |
| unambiguous semidirect product | D1825⋊C3 |
| Fitting, derived, Hall | C25×C73 ⋊ C2×C3 |
| Hall | C25×C73⋊C3 ⋊ C2 |
| Hall | D1825 ⋊ C3 |
| Hall | C73⋊C3 ⋊ D25 |
| Sylow | C73 ⋊ C3×D25 |
| Sylow | C25 ⋊ D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C25×C73 | C2×C3 |
| Frattini | C5 | C5⋊(D73⋊C3) |
| socle | C5×C73 | C3×D5 |
| LCS | G ▷ C25×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,73,5|c^5=e^4,c^a=c^4e,d^a=d^72,e^a=e^4,d^b=d^8342 conjugacy classes — view the full character table.
| maximal subgroup of | #20300469⋊C3, #20300470⋊C3, D25×D73⋊C3, … |
| maximal normal subgroup of | #20300469⋊C3, #20300470⋊C3, D25×D73⋊C3, … |
| maximal quotient of | Dic1825⋊C3, C2×C25⋊(D73⋊C3), C25⋊(#10620321⋊C2), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10950, 12);