Finite Group DatabasebetaFinite Group Databasebeta| order | 8940 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#15688383 |
| Fitting, socle, Hall | C3×C5×C149 ⋊ C4 |
| derived, Hall | C5×C149 ⋊ C3×C4 |
| Hall | C3×C149 ⋊ AGL(1,𝔽5) |
| Sylow | C149 ⋊ C3×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ Dic149 |
| Sylow | C5 ⋊ C3×Dic149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #15688383 |
| commutator, hypocenter | C5×C149 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C149 | C4 |
| LCS | G ▷ C5×C149 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
903 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#15688383, C32×#15688383, C3×C3⋊#15688383 |
| maximal normal subgroup of | C9×#15688383, C32×#15688383 |
| maximal quotient of | C9×#15688383, C32×#15688383, C3×C3⋊#15688383 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8940, 14);