Finite Group DatabasebetaFinite Group Databasebeta| order | 580 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | Dic5×C29 |
| derived, Sylow | C5 ⋊ C4×C29 |
| Hall | C5×C29 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | D5 |
| commutator, hypocenter | C5 | C4×C29 |
| Frattini | C2 | D5×C29 |
| Fitting, socle, prime radical | C2×C5×C29 | C2 |
| cosocle | C2×C5 | C2×C29 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C29 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 580 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C29×#170, #11923906, Dic5×D29, … |
| maximal normal subgroup of | C29×#170, #11923906, Dic5×D29, … |
| maximal quotient of | C29×#168, C2×Dic5×C29, C3×Dic5×C29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(580, 1);