Finite Group DatabasebetaFinite Group Databasebeta| order | 10820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D541⋊C5 |
| unambiguous semidirect product | D541⋊(C2×C5) |
| unambiguous semidirect product | (C2×D541)⋊C5 |
| unambiguous semidirect product | (C541⋊C5)⋊C22 |
| unambiguous semidirect product | (C2×C541⋊C5)⋊C2 |
| Fitting, socle | C2×C541 ⋊ C2×C5 |
| derived, Sylow | C541 ⋊ C22×C5 |
| Hall | C541⋊C5 ⋊ C22 |
| Hall | C2×D541 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D541⋊C5 |
| commutator, cosocle, hypocenter | C541 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C541 | C2×C5 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(D541⋊C3)⋊C5, D3×D541⋊C5, C2×C3×D541⋊C5, … |
| maximal normal subgroup of | C2×(D541⋊C3)⋊C5, C2×C3×D541⋊C5 |
| maximal quotient of | D3×D541⋊C5, C2×C3×D541⋊C5, C2×C3⋊(D541⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10820, 9);