Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | Dic15×C31⋊C3 |
| unambiguous semidirect product | C3⋊(Dic5×C31⋊C3) |
| unambiguous semidirect product | (C31×Dic15)⋊C3 |
| derived | C3×C5×C31 ⋊ C3×C4 |
| Hall | C3×C5×C31⋊C3 ⋊ C4 |
| Hall | C3×C31⋊C3 ⋊ Dic5 |
| Hall | C5×C31 ⋊ C3×Dic3 |
| Sylow | C31 ⋊ C3×Dic15 |
| Sylow | C5 ⋊ Dic3×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D15×C31⋊C3 |
| commutator, hypocenter | C3×C5×C31 | C3×C4 |
| Fitting, socle | C2×C3×C5×C31 | C2×C3 |
| LCS | G ▷ C3×C5×C31 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
234 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×Dic75, Dic15×(C31⋊C3)⋊C5, C5×Dic15×C31⋊C3, … |
| maximal normal subgroup of | Dic15×(C31⋊C3)⋊C5, C5×Dic15×C31⋊C3 |
| maximal quotient of | C31⋊C3×Dic75, C5×Dic15×C31⋊C3, C31⋊C3×C3⋊#1039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 72);