Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C169 · Schur multiplier (H2) = C1 |
| direct product | C9×D5×C169 |
| unambiguous semidirect product | C5⋊(C2×C9×C169) |
| Fitting, Hall | C5×C9×C169 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C9×C169 |
| Hall | C5×C169 ⋊ C2×C9 |
| Hall | C5×C9 ⋊ C2×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9×C169 | D5 |
| commutator, hypocenter | C5 | C2×C9×C169 |
| Frattini | C3×C13 | C3×D5×C13 |
| Fitting | C5×C9×C169 | C2 |
| socle, cosocle | C3×C5×C13 | C2×C3×C13 |
| prime radical | C3×D5×C13 | C3×C13 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C9×C169 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
6084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×AGL(1,𝔽5)×C169, C9×#16809979, C169×C9⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | C9×AGL(1,𝔽5)×C169, C9×#16809979, C169×C9⋊AGL(1,𝔽5), … |
| maximal quotient of | C9×Dic5×C169, C2×C9×D5×C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 7);