Finite Group DatabasebetaFinite Group Databasebeta| order | 17822 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C67 · Schur multiplier (H2) = C1 |
| direct product | C7×D19×C67 |
| unambiguous semidirect product | C19⋊(C2×C7×C67) |
| Fitting, socle, Hall | C7×C19×C67 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C7×C67 |
| Hall | C19×C67 ⋊ C2×C7 |
| Hall | C7×C19 ⋊ C2×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C67 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C7×C67 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C67 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C7×C67 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8911 |
5159 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D19×D67, D7×D19×C67, D19×D469, … |
| maximal normal subgroup of | C7×D19×D67, D7×D19×C67, D19×D469, … |
| maximal quotient of | C7×C67×Dic19, C2×C7×D19×C67 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17822, 3);