Finite Group DatabasebetaFinite Group Databasebeta| order | 8940 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D447 |
| unambiguous semidirect product | (C3×D5)⋊D149 |
| unambiguous semidirect product | (D5×C149)⋊D3 |
| Fitting, socle, derived, Hall | C3×C5×C149 ⋊ C22 |
| Hall | C5×C149 ⋊ C2×D3 |
| Hall | C3×C149 ⋊ C2×D5 |
| Sylow | C149 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×D149 |
| Sylow | C5 ⋊ C2×D447 |
| Sylow | C3 ⋊ D5×D149 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C149 | C22 |
| LCS | G ▷ C3×C5×C149 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
900 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D1341, C3×D5×D447, D15×D447, … |
| maximal normal subgroup of | C3×D5×D447 |
| maximal quotient of | D5×D1341, C3×D5×D447, D15×D447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8940, 26);