Finite Group DatabasebetaFinite Group Databasebeta| order | 11830 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C169 · Schur multiplier (H2) = C1 |
| direct product | C5×D7×C169 |
| unambiguous semidirect product | C7⋊(C2×C5×C169) |
| Fitting, Hall | C5×C7×C169 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C5×C169 |
| Hall | C7×C169 ⋊ C2×C5 |
| Hall | C5×C7 ⋊ C2×C169 |
24 conjugacy classes of subgroups.
4225 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D7×D169, D5×D7×C169, D7×D845, … |
| maximal normal subgroup of | C5×D7×D169, D5×D7×C169, D7×D845, … |
| maximal quotient of | C5×Dic7×C169, C2×C5×D7×C169, C3×C5×D7×C169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11830, 3);