Finite Group DatabasebetaFinite Group Databasebeta| order | 2450 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C49 · Schur multiplier (H2) = C1 |
| direct product | C5×D5×C49 |
| unambiguous semidirect product | C5⋊(C2×C5×C49) |
| Fitting, Hall | C52×C49 ⋊ C2 |
| derived | C5 ⋊ C2×C5×C49 |
| Sylow | C52 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C49 | D5 |
| commutator, hypocenter | C5 | C2×C5×C49 |
| Frattini | C7 | C5×C7×D5 |
| Fitting | C52×C49 | C2 |
| socle | C52×C7 | C2×C7 |
| prime radical | C5×C7×D5 | C7 |
| cosocle | C5×C7 | C2×C5×C7 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C5×C49 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 490 |
980 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C49×A5, C49×C5⋊AGL(1,𝔽11), D5×C49×C11⋊C5, … |
| maximal normal subgroup of | C5×D5×C11×C49, C5×D5×C13×C49 |
| maximal quotient of | C49×C5⋊AGL(1,𝔽11), D5×C49×C11⋊C5, C5×D5×C11×C49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2450, 7);