Finite Group DatabasebetaFinite Group Databasebeta| order | 8060 |
| isoclinism | isoclinic class of #63122 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×#63122 |
| Fitting, socle, Hall | C5×C13×C31 ⋊ C4 |
| derived, Hall | C5×C13 ⋊ C4×C31 |
| Hall | C13×C31 ⋊ AGL(1,𝔽5) |
| Hall | C5×C31 ⋊ #261 |
| Sylow | C13 ⋊ AGL(1,𝔽5)×C31 |
| Sylow | C5 ⋊ C31×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #63122 |
| commutator, hypocenter | C5×C13 | C4×C31 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C31 | C4 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C31 | |
24 conjugacy classes of subgroups.
620 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#63122⋊C3, #37563836, #37563837, … |
| maximal normal subgroup of | C31×#63122⋊C3, #37563836, #37563837, … |
| maximal quotient of | C3×C31×#63122, C31×C3⋊#63122 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8060, 26);