Finite Group DatabasebetaFinite Group Databasebeta| order | 5540 |
| automorphism | Aut(G) order 3058080 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2770 |
| direct product | C2×D1385 |
| unambiguous semidirect product | (C2×C5)⋊D277 |
| unambiguous semidirect product | (C2×C277)⋊D5 |
| Fitting, socle | C2×C5×C277 ⋊ C2 |
| derived, Hall | C5×C277 ⋊ C22 |
| Sylow | C277 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D277 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1385 |
| commutator, hypocenter | C5×C277 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C277 | C2 |
| LCS | G ▷ C5×C277 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
1388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5⋊(D277⋊C3), D3×D1385, C2×D4155, … |
| maximal normal subgroup of | C2×C5⋊(D277⋊C3), C2×C3×D1385, C2×C5×D1385, … |
| maximal quotient of | D3×D1385, C2×D4155, C2×C3×D1385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5540, 13);