Finite Group DatabasebetaFinite Group Databasebeta| order | 5980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | D5×C23×D13 |
| unambiguous semidirect product | (D5×C13)⋊(C2×C23) |
| unambiguous semidirect product | (C5×D13)⋊(C2×C23) |
| unambiguous semidirect product | D65⋊(C2×C23) |
| Fitting, socle, Hall | C5×C13×C23 ⋊ C22 |
| derived, Hall | C5×C13 ⋊ C22×C23 |
| Hall | C13×C23 ⋊ C2×D5 |
| Hall | C5×C23 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D5×C23 |
| Sylow | C5 ⋊ C2×C23×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D5×D13 |
| commutator, hypocenter | C5×C13 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C23 | C22 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C23 | |
40 conjugacy classes of subgroups.
736 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C23×D13⋊C3, C3×D5×C23×D13, C23×D13×D15, … |
| maximal normal subgroup of | D5×C23×D13⋊C3, C3×D5×C23×D13, C5×D5×C23×D13 |
| maximal quotient of | C3×D5×C23×D13, C23×D13×D15, D5×C23×D39, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5980, 25);