Finite Group DatabasebetaFinite Group Databasebeta| order | 10180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D509 |
| unambiguous semidirect product | C509⋊(C22×C5) |
| unambiguous semidirect product | (C2×C509)⋊(C2×C5) |
| Fitting, socle | C2×C5×C509 ⋊ C2 |
| derived, Sylow | C509 ⋊ C22×C5 |
| Hall | C5×C509 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D509 |
| commutator, cosocle, hypocenter | C509 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C509 | C2 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C2×C5 | |
20 conjugacy classes of subgroups.
2560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D509, C2×C3×C5×D509, C2×C5×D1527 |
| maximal normal subgroup of | C2×C3×C5×D509 |
| maximal quotient of | C5×D3×D509, C2×C3×C5×D509, C2×C5×D1527 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10180, 15);