Finite Group DatabasebetaFinite Group Databasebeta| order | 16450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D1645 |
| unambiguous semidirect product | C7⋊(C5⋊D235) |
| unambiguous semidirect product | C47⋊(C5⋊D35) |
| Fitting, socle, derived, Hall | C52×C7×C47 ⋊ C2 |
| Hall | C52×C47 ⋊ D7 |
| Hall | C7×C47 ⋊ C5⋊D5 |
| Hall | C52×C7 ⋊ D47 |
| Sylow | C47 ⋊ C5⋊D35 |
| Sylow | C52 ⋊ D329 |
| Sylow | C7 ⋊ C5⋊D235 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C47 | C2 |
| LCS | G ▷ C52×C7×C47 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8225 |
Polycyclic presentation:
2,5^2,7,47|b^a=b^4,c^a=c^4,d^a=d^6,e^a=e^464114 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1645, D35×D235, D47×C5⋊D35, … |
| maximal normal subgroup of | D5×D1645, D35×D235, D47×C5⋊D35, … |
| maximal quotient of | C7⋊(C47⋊#1039), C2×C5⋊D1645 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16450, 10);