Finite Group DatabasebetaFinite Group Databasebeta| order | 12580 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D37×D85 |
| unambiguous semidirect product | (C5×D37)⋊D17 |
| unambiguous semidirect product | (C17×D37)⋊D5 |
| Fitting, socle, derived, Hall | C5×C17×C37 ⋊ C22 |
| Hall | C17×C37 ⋊ C2×D5 |
| Hall | C5×C37 ⋊ C2×D17 |
| Hall | C5×C17 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D85 |
| Sylow | C17 ⋊ D5×D37 |
| Sylow | C5 ⋊ D17×D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C17×C37 | C22 |
| LCS | G ▷ C5×C17×C37 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
880 conjugacy classes — view the full character table.
| maximal subgroup of | D85×D37⋊C3, C3×D37×D85, D37×D255, … |
| maximal normal subgroup of | D85×D37⋊C3, C3×D37×D85 |
| maximal quotient of | C3×D37×D85, D37×D255, D85×D111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12580, 40);