Finite Group DatabasebetaFinite Group Databasebeta| order | 17822 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D469 |
| unambiguous semidirect product | C7⋊(C19×D67) |
| unambiguous semidirect product | C67⋊(D7×C19) |
| Fitting, socle, Hall | C7×C19×C67 ⋊ C2 |
| derived, Hall | C7×C67 ⋊ C2×C19 |
| Hall | C19×C67 ⋊ D7 |
| Hall | C7×C19 ⋊ D67 |
| Sylow | C67 ⋊ D7×C19 |
| Sylow | C7 ⋊ C19×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D469 |
| commutator, cosocle, hypocenter | C7×C67 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C67 | C2 |
| LCS | G ▷ C7×C67 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8911 |
4484 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C19×D67, D19×D469, D133⋊D67, … |
| maximal normal subgroup of | D7×C19×D67, D19×D469, D133⋊D67, … |
| maximal quotient of | C19×Dic469, C2×C19×D469 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17822, 6);