Finite Group DatabasebetaFinite Group Databasebeta| order | 25308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4294⋊Dic37 |
| derived, Hall | C19×C37 ⋊ C4×C9 |
| Hall | C37×#4294 ⋊ C4 |
| Hall | Dic703 ⋊ C9 |
| Hall | #4294 ⋊ Dic37 |
| Sylow | C37 ⋊ #4294⋊C4 |
| Sylow | C19 ⋊ C9×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | (C19⋊C3)⋊D37 |
| commutator, hypocenter | C19×C37 | C4×C9 |
| Fitting, socle | C2×C3×C19×C37 | C2×C3 |
| LCS | G ▷ C19×C37 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,37,2,3|a^2=e,b^3=f,c^a=c^18,d^a=d^36,c^b=c^71026 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25308, 22);