Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #11927412⋊C9 |
| derived, Hall | C5×C61 ⋊ C4×C9 |
| Hall | C5×C61⋊C9 ⋊ C4 |
| Hall | #11927412 ⋊ C9 |
| Hall | C61⋊C9 ⋊ AGL(1,𝔽5) |
| Sylow | C61 ⋊ C9×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #6923⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #11927412⋊C3 |
| commutator, hypocenter | C5×C61 | C4×C9 |
| Fitting, socle | C3×C5×C61 | C3×C4 |
| prime radical, cosocle | C3×D305 | C2×C3 |
| LCS | G ▷ C5×C61 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5,61,3|a^2=c,b^3=f,d^a=d^2,e^a=e^50,e^b=e^13,d^c=d^4,e^c=e^60120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 29);