Finite Group DatabasebetaFinite Group Databasebeta| order | 12580 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C37 · Schur multiplier (H2) = C1 |
| direct product | C5×C37×#595 |
| Fitting, socle, Hall | C5×C17×C37 ⋊ C4 |
| derived, Sylow | C17 ⋊ C4×C5×C37 |
| Hall | C17×C37 ⋊ C4×C5 |
| Hall | C5×C17 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C37 | #595 |
| commutator, hypocenter | C17 | C4×C5×C37 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C37 | C4 |
| prime radical | C5×D17×C37 | C2 |
| cosocle | D17 | C2×C5×C37 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C5×C37 | |
24 conjugacy classes of subgroups.
1480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#595×C37⋊C3, C3×C5×C37×#595, C5×C37×C3⋊#595 |
| maximal normal subgroup of | C5×#595×C37⋊C3, C3×C5×C37×#595 |
| maximal quotient of | C3×C5×C37×#595, C5×C37×C3⋊#595 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12580, 11);