Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊AGL(1,𝔽61) |
| unambiguous semidirect product | (C3⋊(#6923⋊C3))⋊C5 |
| unambiguous semidirect product | (C3⋊(#6923⋊C5))⋊C3 |
| Fitting, socle, derived | C3×C61 ⋊ C3×C4×C5 |
| Hall | C3×(C61⋊C3)⋊C5 ⋊ C4 |
| Hall | C3⋊(#6923⋊C3) ⋊ C5 |
| Hall | C3×C61⋊C3 ⋊ C4×C5 |
| Hall | C61⋊C5 ⋊ C3×Dic3 |
| Sylow | C61 ⋊ C3×C5×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C61 | C3×C4×C5 |
| prime radical | C3×(D61⋊C3)⋊C5 | C2 |
| cosocle | C3×D61 | C2×C3×C5 |
| LCS | G ▷ C3×C61 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,2,3,61|a^2=d,e^a=e^2,f^a=f^50,f^b=f^13,f^c=f^9,f^d=f^6093 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽61) |
| maximal normal subgroup of | D3×AGL(1,𝔽61) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10980, 103);