Finite Group DatabasebetaFinite Group Databasebeta| order | 25308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D19×#66524⋊C2 |
| unambiguous semidirect product | (C19×#66524⋊C2)⋊C2 |
| unambiguous semidirect product | (D19×#66524)⋊C2 |
| unambiguous semidirect product | (#66524⋊D19)⋊C2 |
| derived, Hall | C19×C37 ⋊ C22×C9 |
| Hall | C19×#66524 ⋊ C22 |
| Hall | D19×D37 ⋊ C9 |
| Hall | #66524 ⋊ C2×D19 |
| Sylow | C37 ⋊ C2×C9×D19 |
| Sylow | C19 ⋊ C2×#66524⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D19×D37⋊C3 |
| commutator, hypocenter | C19×C37 | C22×C9 |
| Fitting, socle | C3×C19×C37 | C22×C3 |
| LCS | G ▷ C19×C37 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
396 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25308, 37);