Finite Group DatabasebetaFinite Group Databasebeta| order | 17450 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C349 · Schur multiplier (H2) = C1 |
| direct product | C5×D5×C349 |
| unambiguous semidirect product | C5⋊(C2×C5×C349) |
| Fitting, socle, Hall | C52×C349 ⋊ C2 |
| derived | C5 ⋊ C2×C5×C349 |
| Sylow | C52 ⋊ C2×C349 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C349 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C5×C349 |
| Frattini | C1 | G |
| Fitting, socle | C52×C349 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C5×C349 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3490 |
6980 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D5×D349, C5×AGL(1,𝔽5)×C349, C5×#20296123, … |
| maximal normal subgroup of | C5×D5×D349, C5×AGL(1,𝔽5)×C349, C5×#20296123, … |
| maximal quotient of | C5×Dic5×C349, C2×C5×D5×C349 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17450, 9);