Finite Group DatabasebetaFinite Group Databasebeta| order | 18780 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20262407⋊C3 |
| Fitting, socle, derived, Hall | C5×C313 ⋊ C3×C4 |
| Hall | #20262407 ⋊ C3 |
| Hall | C5×C313⋊C3 ⋊ C4 |
| Hall | C313⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C313 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic313⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C313 | C3×C4 |
| prime radical | D5×C313⋊C3 | C2 |
| cosocle | D5×C313 | C2×C3 |
| LCS | G ▷ C5×C313 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1565 |
Polycyclic presentation:
2,3,2,5,313|a^2=c,d^a=d^2,e^a=e^312,e^b=e^214,d^c=d^4223 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18780, 17);