Finite Group DatabasebetaFinite Group Databasebeta| order | 8060 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D155 |
| unambiguous semidirect product | (C5×D13)⋊D31 |
| unambiguous semidirect product | (D13×C31)⋊D5 |
| Fitting, socle, derived, Hall | C5×C13×C31 ⋊ C22 |
| Hall | C13×C31 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ C2×D13 |
| Hall | C5×C13 ⋊ C2×D31 |
| Sylow | C31 ⋊ D5×D13 |
| Sylow | C13 ⋊ C2×D155 |
| Sylow | C5 ⋊ D13×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C31 | C22 |
| LCS | G ▷ C5×C13×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
632 conjugacy classes — view the full character table.
| maximal subgroup of | #14559027⋊D5, #14559026⋊D5, D13⋊C3×D155, … |
| maximal normal subgroup of | #14559027⋊D5, #14559026⋊D5, D13⋊C3×D155, … |
| maximal quotient of | C3×D13×D155, D13×D465, D39×D155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8060, 37);