Finite Group DatabasebetaFinite Group Databasebeta| order | 37100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×C7⋊#1035 |
| unambiguous semidirect product | C7⋊(C53×#1035) |
| Fitting, Hall | C7×C25×C53 ⋊ C4 |
| derived, Hall | C7×C25 ⋊ C4×C53 |
| Hall | C25×C53 ⋊ Dic7 |
| Hall | C7×C53 ⋊ #1035 |
| Sylow | C25 ⋊ Dic7×C53 |
| Sylow | C7 ⋊ C53×#1035 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9275 |
2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37100, 17);