Finite Group DatabasebetaFinite Group Databasebeta| order | 12580 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#14578981 |
| Fitting, socle, Hall | C5×C17×C37 ⋊ C4 |
| derived, Hall | C17×C37 ⋊ C4×C5 |
| Hall | C5×C37 ⋊ #595 |
| Hall | C5×C17 ⋊ Dic37 |
| Sylow | C37 ⋊ C5×#595 |
| Sylow | C17 ⋊ C5×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #14578981 |
| commutator, hypocenter | C17×C37 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C37 | C4 |
| prime radical | C5×D17×C37 | C2 |
| cosocle | D17×C37 | C2×C5 |
| LCS | G ▷ C17×C37 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
940 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#14578981⋊C3, C3×C5×#14578981, C5×C3⋊#14578981 |
| maximal normal subgroup of | C5×#14578981⋊C3, C3×C5×#14578981 |
| maximal quotient of | C3×C5×#14578981, C5×C3⋊#14578981 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12580, 14);