Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #14555574⋊C5 |
| Fitting, socle, derived, Hall | C32×C61 ⋊ C4×C5 |
| Hall | C32×C61⋊C5 ⋊ C4 |
| Hall | #14555574 ⋊ C5 |
| Hall | C61⋊C5 ⋊ #157 |
| Sylow | C61 ⋊ C5×#157 |
| Sylow | C32 ⋊ #6923⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C61 | C4×C5 |
| prime radical | C3⋊(C3⋊(D61⋊C5)) | C2 |
| cosocle | C3⋊D183 | C2×C5 |
| LCS | G ▷ C32×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,3^2,61|a^2=c,d^a=de,e^a=de^2,f^a=f^50,f^b=f^9,d^c=d^2,e^c=e^2,f^c=f^6057 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 117);