Finite Group DatabasebetaFinite Group Databasebeta| order | 17822 |
| isoclinism | isoclinic class of D133 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×D133 |
| unambiguous semidirect product | C7⋊(D19×C67) |
| unambiguous semidirect product | C19⋊(D7×C67) |
| Fitting, socle, Hall | C7×C19×C67 ⋊ C2 |
| derived, Hall | C7×C19 ⋊ C2×C67 |
| Hall | C19×C67 ⋊ D7 |
| Hall | C7×C67 ⋊ D19 |
| Sylow | C19 ⋊ D7×C67 |
| Sylow | C7 ⋊ D19×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | D133 |
| commutator, cosocle, hypocenter | C7×C19 | C2×C67 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C67 | C2 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C67 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8911 |
4556 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D67×D133, D7×D19×C67, D133⋊D67, … |
| maximal normal subgroup of | D67×D133, D7×D19×C67, D133⋊D67, … |
| maximal quotient of | C67×Dic133, C2×C67×D133 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17822, 7);