Finite Group DatabasebetaFinite Group Databasebeta| order | 37940 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D1897 |
| unambiguous semidirect product | (C7×D5)⋊D271 |
| unambiguous semidirect product | (D5×C271)⋊D7 |
| Fitting, socle, derived, Hall | C5×C7×C271 ⋊ C22 |
| Hall | C7×C271 ⋊ C2×D5 |
| Hall | C5×C271 ⋊ C2×D7 |
| Sylow | C271 ⋊ D5×D7 |
| Hall | C5×C7 ⋊ C2×D271 |
| Sylow | C7 ⋊ D5×D271 |
| Sylow | C5 ⋊ C2×D1897 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C271 | C22 |
| LCS | G ▷ C5×C7×C271 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9485 |
3800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37940, 28);