Finite Group DatabasebetaFinite Group Databasebeta| order | 9490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D365 |
| unambiguous semidirect product | C5⋊(C13×D73) |
| unambiguous semidirect product | C73⋊(D5×C13) |
| Fitting, socle, Hall | C5×C13×C73 ⋊ C2 |
| derived, Hall | C5×C73 ⋊ C2×C13 |
| Hall | C13×C73 ⋊ D5 |
| Sylow | C73 ⋊ D5×C13 |
| Hall | C5×C13 ⋊ D73 |
| Sylow | C5 ⋊ C13×D73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D365 |
| commutator, cosocle, hypocenter | C5×C73 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C73 | C2 |
| LCS | G ▷ C5×C73 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
2392 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×#13091732, C13×#13091733, #34039423, … |
| maximal normal subgroup of | C13×#13091732, C13×#13091733, #34039423, … |
| maximal quotient of | C13×Dic365, C2×C13×D365, C3×C13×D365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9490, 6);