Finite Group DatabasebetaFinite Group Databasebeta| order | 8940 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic447 |
| unambiguous semidirect product | C3⋊(C5×Dic149) |
| derived, Hall | C3×C149 ⋊ C4×C5 |
| Hall | C3×C5×C149 ⋊ C4 |
| Hall | C5×C149 ⋊ Dic3 |
| Sylow | C149 ⋊ C5×Dic3 |
| Hall | C3×C5 ⋊ Dic149 |
| Sylow | C3 ⋊ C5×Dic149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D447 |
| commutator, hypocenter | C3×C149 | C4×C5 |
| Frattini | C2 | C5×D447 |
| Fitting, socle | C2×C3×C5×C149 | C2 |
| LCS | G ▷ C3×C149 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
2250 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic1341, C5×C3⋊Dic447, C3×C5×Dic447 |
| maximal normal subgroup of | C3×C5×Dic447 |
| maximal quotient of | C5×Dic1341, C5×C3⋊Dic447, C3×C5×Dic447 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8940, 6);