Finite Group DatabasebetaFinite Group Databasebeta| order | 610 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C1 |
| direct product | D5×C61 |
| unambiguous semidirect product | C5⋊(C2×C61) |
| Fitting, socle, Hall | C5×C61 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C5×C61 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C61 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 305 |
244 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×C61, #11927414, D5×D61, … |
| maximal normal subgroup of | AGL(1,𝔽5)×C61, #11927414, D5×D61, … |
| maximal quotient of | Dic5×C61, C2×D5×C61, C3×D5×C61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(610, 3);