Finite Group DatabasebetaFinite Group Databasebeta| order | 12580 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17×C37 · Schur multiplier (H2) = C1 |
| direct product | C17×Dic5×C37 |
| derived, Sylow | C5 ⋊ C4×C17×C37 |
| Hall | C5×C17×C37 ⋊ C4 |
| Hall | C5×C37 ⋊ C4×C17 |
| Hall | C5×C17 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17×C37 | D5 |
| commutator, hypocenter | C5 | C4×C17×C37 |
| Frattini | C2 | D5×C17×C37 |
| Fitting, socle, prime radical | C2×C5×C17×C37 | C2 |
| cosocle | C2×C5 | C2×C17×C37 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C17×C37 | |
24 conjugacy classes of subgroups.
5032 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C17×Dic5×C37, C17×C37×Dic15, C17×Dic5×C37⋊C3 |
| maximal normal subgroup of | C3×C17×Dic5×C37, C17×Dic5×C37⋊C3 |
| maximal quotient of | C3×C17×Dic5×C37, C17×C37×Dic15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12580, 5);