Finite Group DatabasebetaFinite Group Databasebeta| order | 25308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D171⋊D37 |
| unambiguous semidirect product | D333⋊D19 |
| unambiguous semidirect product | D703⋊D9 |
| Fitting, derived, Hall | C9×C19×C37 ⋊ C22 |
| Hall | C19×C37 ⋊ C2×D9 |
| Hall | C9×C37 ⋊ C2×D19 |
| Hall | C9×C19 ⋊ C2×D37 |
| Sylow | C37 ⋊ D9×D19 |
| Sylow | C19 ⋊ D9×D37 |
| Sylow | C9 ⋊ D19×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C19×C37 | C22 |
| Frattini | C3 | D57⋊D37 |
| socle | C3×C19×C37 | C2×D3 |
| LCS | G ▷ C9×C19×C37 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,19,37,3|c^3=f^2,d^a=d^18,e^a=e^36,c^b=c^2f,d^b=d^18,f^b=f^21632 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25308, 60);