Finite Group DatabasebetaFinite Group Databasebeta| order | 25308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#27162552 |
| derived, Hall | C19×C37 ⋊ C22×C9 |
| Hall | #20263540 ⋊ C22 |
| Hall | C2×C19×D37 ⋊ C9 |
| Hall | C2×D37 ⋊ #4294 |
| Sylow | C37 ⋊ C22×#4294 |
| Sylow | C19 ⋊ C2×#66524⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #16862422 |
| commutator, hypocenter | C19×C37 | C22×C9 |
| Frattini | C3 | C2×#16862422 |
| Fitting, socle | C2×C3×C19×C37 | C2×C3 |
| LCS | G ▷ C19×C37 | |
| UCS | C1 ◁ C2×C3 | |
60 conjugacy classes of subgroups.
792 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25308, 45);