Finite Group DatabasebetaFinite Group Databasebeta| order | 36260 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic1813 |
| unambiguous semidirect product | C49⋊(C5×Dic37) |
| derived, Hall | C37×C49 ⋊ C4×C5 |
| Hall | C5×C37×C49 ⋊ C4 |
| Hall | C5×C49 ⋊ Dic37 |
| Hall | C5×C37 ⋊ Dic49 |
| Sylow | C49 ⋊ C5×Dic37 |
| Sylow | C37 ⋊ C5×Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1813 |
| commutator, hypocenter | C37×C49 | C4×C5 |
| Frattini | C2×C7 | C5×D259 |
| Fitting | C2×C5×C37×C49 | C2 |
| socle, prime radical | C2×C5×C7×C37 | D7 |
| cosocle | C2×C37×C49 | C2×C5 |
| LCS | G ▷ C37×C49 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36260 |
9080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36260, 4);