Finite Group DatabasebetaFinite Group Databasebeta| order | 18130 |
| isoclinism | isoclinic class of D185 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D185 |
| unambiguous semidirect product | C5⋊(C49×D37) |
| unambiguous semidirect product | C37⋊(D5×C49) |
| Fitting, Hall | C5×C37×C49 ⋊ C2 |
| derived, Hall | C5×C37 ⋊ C2×C49 |
| Hall | C37×C49 ⋊ D5 |
| Hall | C5×C49 ⋊ D37 |
| Sylow | C37 ⋊ D5×C49 |
| Sylow | C5 ⋊ C49×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D185 |
| commutator, hypocenter | C5×C37 | C2×C49 |
| Frattini | C7 | C7×D185 |
| Fitting | C5×C37×C49 | C2 |
| socle, cosocle | C5×C7×C37 | C2×C7 |
| prime radical | C7×D185 | C7 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C49 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9065 |
4606 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C49×#10625191, C49×#10625192, C49⋊#10625191, … |
| maximal normal subgroup of | C49×#10625191, C49×#10625192, C49⋊#10625191, … |
| maximal quotient of | C49×Dic185, C2×C49×D185 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18130, 6);