Finite Group DatabasebetaFinite Group Databasebeta| order | 10180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D509 |
| unambiguous semidirect product | (D5×C509)⋊C2 |
| unambiguous semidirect product | (C5×D509)⋊C2 |
| unambiguous semidirect product | D2545⋊C2 |
| Fitting, socle, derived, Hall | C5×C509 ⋊ C22 |
| Sylow | C509 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D509 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C509 | C22 |
| LCS | G ▷ C5×C509 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
1024 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×D509, D15×D509, D5×D1527, … |
| maximal normal subgroup of | C3×D5×D509 |
| maximal quotient of | C3×D5×D509, D15×D509, D5×D1527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10180, 12);