Finite Group DatabasebetaFinite Group Databasebeta| order | 36550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C43 · Schur multiplier (H2) = C1 |
| direct product | C5×C43×D85 |
| unambiguous semidirect product | C5⋊(C5×D17×C43) |
| unambiguous semidirect product | C17⋊(C5×D5×C43) |
| Fitting, socle, Hall | C52×C17×C43 ⋊ C2 |
| derived | C5×C17 ⋊ C2×C5×C43 |
| Hall | C52×C43 ⋊ D17 |
| Hall | C17×C43 ⋊ C5×D5 |
| Hall | C52×C17 ⋊ C2×C43 |
| Sylow | C52 ⋊ D17×C43 |
| Sylow | C17 ⋊ C5×D5×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C43 | D85 |
| commutator, cosocle, hypocenter | C5×C17 | C2×C5×C43 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C43 | C2 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C5×C43 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7310 |
9460 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36550, 15);