Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C169 · Schur multiplier (H2) = C3 |
| direct product | C32×D5×C169 |
| unambiguous semidirect product | C5⋊(C2×C32×C169) |
| Fitting, Hall | C32×C5×C169 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C32×C169 |
| Hall | C5×C169 ⋊ C2×C32 |
| Hall | C32×C5 ⋊ C2×C169 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
6084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×AGL(1,𝔽5)×C169, C32×#16809979, C32×D5×D169, … |
| maximal normal subgroup of | C32×AGL(1,𝔽5)×C169, C32×#16809979, C32×D5×D169, … |
| maximal quotient of | C32×Dic5×C169, C2×C32×D5×C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 23);