Finite Group DatabasebetaFinite Group Databasebeta| order | 6498 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C19 · Schur multiplier (H2) = C1 |
| direct product | C2×C19×#4294 |
| derived | C19 ⋊ C2×C9×C19 |
| Hall | C2×C192 ⋊ C9 |
| Sylow | C192 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C19 | C19⋊C3 |
| commutator, hypocenter | C19 | C2×C9×C19 |
| Frattini | C3 | C2×C19×C19⋊C3 |
| Fitting, socle | C2×C3×C192 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C3×C19 | |
48 conjugacy classes of subgroups.
1026 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#4294⋊C4, #4294⋊Dic19, Dic19×#4294, … |
| maximal normal subgroup of | C19×#4294⋊C4, #4294⋊Dic19, Dic19×#4294, … |
| maximal quotient of | C4×C19×#4294, C22×C19×#4294, D5×C19×#4294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6498, 28);