Finite Group DatabasebetaFinite Group Databasebeta| order | 10980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived | C3×C61 ⋊ C22×C3×C5 |
| Hall | C3×(C61⋊C3)⋊C5 ⋊ C22 |
| Hall | D3×D61⋊C3 ⋊ C5 |
| Hall | C3×C61⋊C3 ⋊ C22×C5 |
| Hall | C61⋊C5 ⋊ C2×C3×D3 |
| Sylow | C61 ⋊ C2×C3×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C61 | C22×C3×C5 |
| LCS | G ▷ C3×C61 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
96 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, 104);