Finite Group DatabasebetaFinite Group Databasebeta| order | 5980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | D5×C13×D23 |
| unambiguous semidirect product | (D5×C23)⋊(C2×C13) |
| unambiguous semidirect product | (C5×D23)⋊(C2×C13) |
| unambiguous semidirect product | D115⋊(C2×C13) |
| Fitting, socle, Hall | C5×C13×C23 ⋊ C22 |
| derived, Hall | C5×C23 ⋊ C22×C13 |
| Hall | C13×C23 ⋊ C2×D5 |
| Hall | C5×C13 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D5×C13 |
| Sylow | C5 ⋊ C2×C13×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D5×D23 |
| commutator, hypocenter | C5×C23 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C23 | C22 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C13 | |
40 conjugacy classes of subgroups.
676 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C13⋊C3×D23, C3×D5×C13×D23, C13×D15×D23, … |
| maximal normal subgroup of | D5×C13⋊C3×D23, C3×D5×C13×D23, C5×D5×C13×D23 |
| maximal quotient of | C3×D5×C13×D23, C13×D15×D23, D5×C13×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5980, 21);