Finite Group DatabasebetaFinite Group Databasebeta| order | 11830 |
| isoclinism | isoclinic class of D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C169 · Schur multiplier (H2) = C1 |
| direct product | D35×C169 |
| unambiguous semidirect product | C5⋊(D7×C169) |
| unambiguous semidirect product | C7⋊(D5×C169) |
| Fitting, Hall | C5×C7×C169 ⋊ C2 |
| derived, Hall | C5×C7 ⋊ C2×C169 |
| Hall | C7×C169 ⋊ D5 |
| Hall | C5×C169 ⋊ D7 |
| Sylow | C7 ⋊ D5×C169 |
| Sylow | C5 ⋊ D7×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C169 | D35 |
| commutator, hypocenter | C5×C7 | C2×C169 |
| Frattini | C13 | C13×D35 |
| Fitting | C5×C7×C169 | C2 |
| socle, cosocle | C5×C7×C13 | C2×C13 |
| prime radical | C13×D35 | C13 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C169 | |
24 conjugacy classes of subgroups.
3211 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D35×D169, D5×D7×C169, D35⋊D169, … |
| maximal normal subgroup of | D35×D169, D5×D7×C169, D35⋊D169, … |
| maximal quotient of | Dic35×C169, C2×D35×C169, C3×D35×C169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11830, 7);