Finite Group DatabasebetaFinite Group Databasebeta| order | 2610 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C29 · Schur multiplier (H2) = C1 |
| direct product | C9×D5×C29 |
| unambiguous semidirect product | C5⋊(C2×C9×C29) |
| Fitting, Hall | C5×C9×C29 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C9×C29 |
| Hall | C5×C29 ⋊ C2×C9 |
| Hall | C5×C9 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9×C29 | D5 |
| commutator, hypocenter | C5 | C2×C9×C29 |
| Frattini | C3 | C3×D5×C29 |
| Fitting | C5×C9×C29 | C2 |
| socle | C3×C5×C29 | C2×C3 |
| prime radical | C3×D5×C29 | C3 |
| cosocle | C3×C5 | C2×C3×C29 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C9×C29 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1305 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,2,3,4,5,6,7,8,9)(10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(11,14)(12,13)1044 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C29×D25, C5×C9×D5×C29, C9×C29×C5⋊D5, … |
| maximal normal subgroup of | C5×C9×D5×C29, C7×C9×D5×C29, C9×D5×C29⋊C7, … |
| maximal quotient of | C9×C29×D25, C5×C9×D5×C29, C9×C29×C5⋊D5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2610, 3);