Finite Group DatabasebetaFinite Group Databasebeta| order | 10860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C3×C181 ⋊ C22×C5 |
| Hall | C3×C181⋊C5 ⋊ C22 |
| Hall | D3×D181 ⋊ C5 |
| Hall | C181⋊C5 ⋊ C2×D3 |
| Sylow | C181 ⋊ C2×C5×D3 |
| Sylow | C3 ⋊ C2×D181⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C181 | C22×C5 |
| LCS | G ▷ C3×C181 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
84 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D181⋊C5, D3×(D181⋊C3)⋊C5, C3×D3×D181⋊C5, … |
| maximal normal subgroup of | D3×(D181⋊C3)⋊C5, C3×D3×D181⋊C5 |
| maximal quotient of | D9×D181⋊C5, C3×D3×D181⋊C5, D3×C3⋊(D181⋊C5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10860, 24);