Finite Group DatabasebetaFinite Group Databasebeta| order | 37675 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C137 · Schur multiplier (H2) = C1 |
| direct product | C137×C11⋊C25 |
| unambiguous semidirect product | C11⋊(C25×C137) |
| unambiguous semidirect product | (C11×C137)⋊C25 |
| derived, Sylow | C11 ⋊ C25×C137 |
| Hall | C11×C137 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C137 | C11⋊C5 |
| commutator, hypocenter | C11 | C25×C137 |
| Frattini | C5 | C11⋊C5×C137 |
| Fitting, socle, prime radical | C5×C11×C137 | C5 |
| cosocle | C5×C11 | C5×C137 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C5×C137 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37675 |
4795 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37675, 2);