Finite Group DatabasebetaFinite Group Databasebeta| order | 11780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊(Dic31⋊C5) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊Dic19 |
| unambiguous semidirect product | Dic589⋊C5 |
| derived, Hall | C19×C31 ⋊ C4×C5 |
| Hall | C19×ΓL(1,𝔽32) ⋊ C4 |
| Hall | Dic589 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ Dic19 |
| Sylow | C31 ⋊ C5×Dic19 |
| Sylow | C19 ⋊ Dic31⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C19⋊(D31⋊C5) |
| commutator, hypocenter | C19×C31 | C4×C5 |
| Fitting, socle, cosocle | C2×C19×C31 | C2×C5 |
| prime radical | C2×C19×ΓL(1,𝔽32) | C2 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,19,31,2|a^2=e,c^a=c^18,d^a=d^30,d^b=d^16224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11780, 12);