Finite Group DatabasebetaFinite Group Databasebeta| order | 8780 |
| automorphism | Aut(G) order 7691280 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4390 |
| direct product | C2×D2195 |
| unambiguous semidirect product | (C2×C5)⋊D439 |
| unambiguous semidirect product | (C2×C439)⋊D5 |
| Fitting, socle | C2×C5×C439 ⋊ C2 |
| derived, Hall | C5×C439 ⋊ C22 |
| Sylow | C439 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D439 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2195 |
| commutator, hypocenter | C5×C439 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C439 | C2 |
| LCS | G ▷ C5×C439 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5⋊(D439⋊C3), D3×D2195, C2×C3×D2195, … |
| maximal normal subgroup of | C2×C5⋊(D439⋊C3), C2×C3×D2195, D8780 |
| maximal quotient of | D3×D2195, C2×C3×D2195, C2×D6585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8780, 9);