Finite Group DatabasebetaFinite Group Databasebeta| order | 7334 |
| isoclinism | isoclinic class of D193 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D193 |
| unambiguous semidirect product | C193⋊(C2×C19) |
| Fitting, socle, Hall | C19×C193 ⋊ C2 |
| derived, Sylow | C193 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D193 |
| commutator, hypocenter | C193 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C193 | C2 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C19 | |
8 conjugacy classes of subgroups.
1862 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#11715871, C19⋊#11715871, D19×D193, … |
| maximal normal subgroup of | C19×#11715871, C19⋊#11715871, D19×D193, … |
| maximal quotient of | C19×Dic193, C2×C19×D193, C3×C19×D193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7334, 2);