Finite Group DatabasebetaFinite Group Databasebeta| order | 520 |
| isoclinism | isoclinic class of D65 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D65 |
| Fitting, socle | C22×C5×C13 ⋊ C2 |
| derived, Hall | C5×C13 ⋊ C23 |
| Sylow | C13 ⋊ C22×D5 |
| Sylow | C5 ⋊ C22×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D65 |
| commutator, cosocle, hypocenter | C5×C13 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C13 | C2 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C22 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 260 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #11760103, #11760149, C22⋊#63122, … |
| maximal normal subgroup of | #11760103, #11760149, C22⋊#63122, … |
| maximal quotient of | C2×Dic130, C2×C4×D65, C2×D260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(520, 48);