Finite Group DatabasebetaFinite Group Databasebeta| order | 5980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D13×D23 |
| unambiguous semidirect product | (C23×D13)⋊(C2×C5) |
| unambiguous semidirect product | (C13×D23)⋊(C2×C5) |
| unambiguous semidirect product | D299⋊(C2×C5) |
| Fitting, socle, Hall | C5×C13×C23 ⋊ C22 |
| derived, Hall | C13×C23 ⋊ C22×C5 |
| Hall | C5×C23 ⋊ C2×D13 |
| Hall | C5×C13 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C5×D13 |
| Sylow | C13 ⋊ C2×C5×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D13×D23 |
| commutator, hypocenter | C13×C23 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C23 | C22 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
520 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D23×D13⋊C3, C3×C5×D13×D23, C5×D23×D39, … |
| maximal normal subgroup of | C5×D23×D13⋊C3, C3×C5×D13×D23, C25×D13×D23, … |
| maximal quotient of | C3×C5×D13×D23, C5×D23×D39, C5×D13×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5980, 12);