Finite Group DatabasebetaFinite Group Databasebeta| order | 37084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D73×D127 |
| unambiguous semidirect product | (C127×D73)⋊C2 |
| unambiguous semidirect product | (C73×D127)⋊C2 |
| unambiguous semidirect product | D9271⋊C2 |
| Fitting, socle, derived, Hall | C73×C127 ⋊ C22 |
| Sylow | C127 ⋊ C2×D73 |
| Sylow | C73 ⋊ C2×D127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C73×C127 | C22 |
| LCS | G ▷ C73×C127 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9271 |
2470 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37084, 8);