Finite Group DatabasebetaFinite Group Databasebeta| order | 5580 |
| isoclinism | isoclinic class of D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | C2×C31×D45 |
| unambiguous semidirect product | (C2×C5)⋊(D9×C31) |
| unambiguous semidirect product | (C2×C9)⋊(D5×C31) |
| Fitting | C2×C5×C9×C31 ⋊ C2 |
| derived, Hall | C5×C9 ⋊ C22×C31 |
| Hall | C5×C9×C31 ⋊ C22 |
| Hall | C9×C31 ⋊ C2×D5 |
| Hall | C5×C31 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D5×C31 |
| Sylow | C5 ⋊ C2×D9×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D45 |
| commutator, hypocenter | C5×C9 | C22×C31 |
| Frattini | C3 | C2×D15×C31 |
| Fitting | C2×C5×C9×C31 | C2 |
| socle | C2×C3×C5×C31 | D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C2×C31 | |
60 conjugacy classes of subgroups.
1488 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C31×D225, C2×D45×ΓL(1,𝔽32), D5×C31×D45, … |
| maximal normal subgroup of | C2×D45×ΓL(1,𝔽32), C2×C5×C31×D45 |
| maximal quotient of | C2×C31×D225, D5×C31×D45, C2×C31×C5⋊D45, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5580, 54);