Finite Group DatabasebetaFinite Group Databasebeta| order | 37450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D3745 |
| unambiguous semidirect product | C5⋊(C5×D749) |
| unambiguous semidirect product | C7⋊(C5×D535) |
| unambiguous semidirect product | C107⋊(C5×D35) |
| Fitting, socle, Hall | C52×C7×C107 ⋊ C2 |
| derived | C5×C7×C107 ⋊ C2×C5 |
| Hall | C52×C107 ⋊ D7 |
| Hall | C7×C107 ⋊ C5×D5 |
| Hall | C52×C7 ⋊ D107 |
| Sylow | C107 ⋊ C5×D35 |
| Sylow | C52 ⋊ D749 |
| Sylow | C7 ⋊ C5×D535 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3745 |
| commutator, cosocle, hypocenter | C5×C7×C107 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C107 | C2 |
| LCS | G ▷ C5×C7×C107 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7490 |
9370 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37450, 16);