Finite Group DatabasebetaFinite Group Databasebeta| order | 11830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D845 |
| unambiguous semidirect product | C5⋊(C7×D169) |
| unambiguous semidirect product | C169⋊(C7×D5) |
| Fitting, Hall | C5×C7×C169 ⋊ C2 |
| derived, Hall | C5×C169 ⋊ C2×C7 |
| Hall | C7×C169 ⋊ D5 |
| Sylow | C169 ⋊ C7×D5 |
| Hall | C5×C7 ⋊ D169 |
| Sylow | C5 ⋊ C7×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D845 |
| commutator, cosocle, hypocenter | C5×C169 | C2×C7 |
| Frattini | C13 | C7×D65 |
| Fitting | C5×C7×C169 | C2 |
| socle | C5×C7×C13 | D13 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
2968 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#16809980, C7×#16809981, C7⋊#16809980, … |
| maximal normal subgroup of | C7×#16809980, C7×#16809981, C7⋊#16809980, … |
| maximal quotient of | C7×Dic845, C2×C7×D845, C3×C7×D845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11830, 6);