Finite Group DatabasebetaFinite Group Databasebeta| order | 25308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C19×C37 ⋊ C4×C9 |
| Hall | C19×#66524 ⋊ C4 |
| Hall | Dic703 ⋊ C9 |
| Hall | #66524 ⋊ Dic19 |
| Sylow | C37 ⋊ C9×Dic19 |
| Sylow | C19 ⋊ #13050607 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | (C37⋊C3)⋊D19 |
| 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,d^b=d^26882 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25308, 21);