Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C31 · Schur multiplier (H2) = C3 |
| direct product | C5×C31×#157 |
| Fitting, socle, Hall | C32×C5×C31 ⋊ C4 |
| derived, Sylow | C32 ⋊ C4×C5×C31 |
| Hall | C32×C31 ⋊ C4×C5 |
| Hall | C32×C5 ⋊ C4×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C31 | #157 |
| commutator, hypocenter | C32 | C4×C5×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C31 | C4 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C5×C31 | |
40 conjugacy classes of subgroups.
930 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 156);