Finite Group DatabasebetaFinite Group Databasebeta| order | 16450 |
| isoclinism | isoclinic class of C5⋊D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47 · Schur multiplier (H2) = C5 |
| direct product | C47×C5⋊D35 |
| unambiguous semidirect product | C5⋊(C47×D35) |
| unambiguous semidirect product | C7⋊(C47×C5⋊D5) |
| Fitting, socle, Hall | C52×C7×C47 ⋊ C2 |
| derived, Hall | C52×C7 ⋊ C2×C47 |
| Hall | C52×C47 ⋊ D7 |
| Hall | C7×C47 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D7×C47 |
| Sylow | C7 ⋊ C47×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | C5⋊D35 |
| commutator, cosocle, hypocenter | C52×C7 | C2×C47 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C47 | C2 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C47 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8225 |
4183 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×C47×D35, D235⋊D35, D47×C5⋊D35, … |
| maximal normal subgroup of | D5×C47×D35, D235⋊D35, D47×C5⋊D35, … |
| maximal quotient of | C47×C7⋊#1039, C2×C47×C5⋊D35 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16450, 11);