Finite Group DatabasebetaFinite Group Databasebeta| order | 25308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×#4296⋊C4 |
| unambiguous semidirect product | #4296⋊(C4×C37) |
| derived, Sylow | C19 ⋊ C4×C9×C37 |
| Hall | C37×#4296 ⋊ C4 |
| Hall | C37×Dic19 ⋊ C9 |
| Hall | C19×C37 ⋊ C4×C9 |
| Hall | #4296 ⋊ C4×C37 |
| Hall | Dic19 ⋊ C9×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | AGL(1,𝔽19) |
| commutator, hypocenter | C19 | C4×C9×C37 |
| Frattini | C2 | C37×AGL(1,𝔽19) |
| Fitting, socle | C2×C19×C37 | C2×C9 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C37 | |
36 conjugacy classes of subgroups.
1406 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25308, 79);