Finite Group DatabasebetaFinite Group Databasebeta| order | 530 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D53 |
| unambiguous semidirect product | C53⋊(C2×C5) |
| Fitting, socle, Hall | C5×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D53 |
| commutator, cosocle, hypocenter | C53 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C53 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 265 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#6157, #11761508, D5×D53, … |
| maximal normal subgroup of | C5×#6157, #11761508, D5×D53, … |
| maximal quotient of | C5×Dic53, C2×C5×D53, C3×C5×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(530, 2);