Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C61 ⋊ C3×C4×C5 |
| derived, Sylow | C61 ⋊ C32×C4×C5 |
| Hall | C3×(C61⋊C3)⋊C5 ⋊ C4 |
| Hall | C3×#6923⋊C3 ⋊ C5 |
| Hall | #6923⋊C5 ⋊ C32 |
| Hall | C3×C61⋊C3 ⋊ C4×C5 |
| Hall | C61⋊C5 ⋊ C32×C4 |
| Hall | #6923 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | AGL(1,𝔽61) |
| commutator, hypocenter | C61 | C32×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C61 | C3×C4×C5 |
| prime radical | C3×(D61⋊C3)⋊C5 | C2 |
| cosocle | D61 | C2×C32×C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
183 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, 102);