Finite Group DatabasebetaFinite Group Databasebeta| order | 520 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C22×D5×C13 |
| unambiguous semidirect product | C5⋊(C23×C13) |
| unambiguous semidirect product | (C2×C5)⋊(C22×C13) |
| Fitting, socle | C22×C5×C13 ⋊ C2 |
| derived, Sylow | C5 ⋊ C23×C13 |
| Hall | C5×C13 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C13 | D5 |
| commutator, cosocle, hypocenter | C5 | C23×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C13 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C22×C13 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 260 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #11760102, C13×#685, C13×C22⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | #11760102, C13×#685, C13×C22⋊AGL(1,𝔽5), … |
| maximal quotient of | C2×C13×Dic10, C2×C4×D5×C13, C2×C13×D20, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(520, 47);