Finite Group DatabasebetaFinite Group Databasebeta| order | 8060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic155 |
| unambiguous semidirect product | C31⋊(C13×Dic5) |
| derived, Hall | C5×C31 ⋊ C4×C13 |
| Hall | C5×C13×C31 ⋊ C4 |
| Hall | C13×C31 ⋊ Dic5 |
| Hall | C5×C13 ⋊ Dic31 |
| Sylow | C31 ⋊ C13×Dic5 |
| Sylow | C5 ⋊ C13×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D155 |
| commutator, hypocenter | C5×C31 | C4×C13 |
| Frattini | C2 | C13×D155 |
| Fitting, socle | C2×C5×C13×C31 | C2 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C2×C13 | |
24 conjugacy classes of subgroups.
2054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×Dic155, C13×Dic465, C13×(C31⋊C3)⋊Dic5, … |
| maximal normal subgroup of | C3×C13×Dic155, C13×(C31⋊C3)⋊Dic5, C13⋊C3×Dic155, … |
| maximal quotient of | C3×C13×Dic155, C13×Dic465 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8060, 7);