Finite Group DatabasebetaFinite Group Databasebeta| order | 2610 |
| isoclinism | isoclinic class of D261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D261 |
| unambiguous semidirect product | C9⋊(C5×D29) |
| unambiguous semidirect product | C29⋊(C5×D9) |
| Fitting, Hall | C5×C9×C29 ⋊ C2 |
| derived, Hall | C9×C29 ⋊ C2×C5 |
| Hall | C5×C29 ⋊ D9 |
| Hall | C5×C9 ⋊ D29 |
| Sylow | C29 ⋊ C5×D9 |
| Sylow | C9 ⋊ C5×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D261 |
| commutator, cosocle, hypocenter | C9×C29 | C2×C5 |
| Frattini | C3 | C5×D87 |
| Fitting | C5×C9×C29 | C2 |
| socle | C3×C5×C29 | D3 |
| LCS | G ▷ C9×C29 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1305 |
660 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×D261, C52×D261, C5×D1305, … |
| maximal normal subgroup of | C25×D261, C52×D261, C5×C7×D261, … |
| maximal quotient of | C25×D261, C52×D261, C5×D1305, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2610, 6);