Finite Group DatabasebetaFinite Group Databasebeta| order | 11830 |
| isoclinism | isoclinic class of D65 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C7×C13×D65 |
| unambiguous semidirect product | C5⋊(C7×C13×D13) |
| unambiguous semidirect product | C13⋊(C7×D5×C13) |
| Fitting, socle, Hall | C5×C7×C132 ⋊ C2 |
| derived | C5×C13 ⋊ C2×C7×C13 |
| Hall | C7×C132 ⋊ D5 |
| Hall | C5×C132 ⋊ C2×C7 |
| Sylow | C132 ⋊ C7×D5 |
| Hall | C5×C7 ⋊ C13×D13 |
| Sylow | C5 ⋊ C7×C13×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C13 | D65 |
| commutator, cosocle, hypocenter | C5×C13 | C2×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C132 | C2 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C7×C13 | |
56 conjugacy classes of subgroups.
3094 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C13×#63122, C7×C13×#63121, C7×#16810005, … |
| maximal normal subgroup of | C7×C13×#63122, C7×C13×#63121, C7×#16810005, … |
| maximal quotient of | C7×C13×Dic65, C2×C7×C13×D65, C3×C7×C13×D65, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11830, 20);