Finite Group DatabasebetaFinite Group Databasebeta| order | 520 |
| isoclinism | isoclinic class of #63118 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#63118 |
| unambiguous semidirect product | D13⋊Dic5 |
| Fitting, socle | C2×C5×C13 ⋊ C4 |
| derived, Hall | C5×C13 ⋊ C2×C4 |
| Sylow | C13 ⋊ C2×Dic5 |
| Sylow | C5 ⋊ C2×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #63118 |
| commutator, hypocenter | C5×C13 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C13 | C4 |
| prime radical | C2×C5×D13 | C2 |
| cosocle | C5×D13 | C22 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 130 |
46 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×#261, (C2×#261)⋊D5, #11760179, … |
| maximal normal subgroup of | Dic5×#261, (C2×#261)⋊D5, #11760179, … |
| maximal quotient of | D13⋊#168, #11760220, C4×#63118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(520, 44);