Finite Group DatabasebetaFinite Group Databasebeta| order | 18924 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×(C19⋊C3)⋊C4 |
| unambiguous semidirect product | (C19⋊C3)⋊(C4×C83) |
| unambiguous semidirect product | Dic19⋊(C3×C83) |
| unambiguous semidirect product | (Dic19×C83)⋊C3 |
| derived, Sylow | C19 ⋊ C3×C4×C83 |
| Hall | Dic19×C83 ⋊ C3 |
| Hall | C19⋊C3×C83 ⋊ C4 |
| Hall | C19×C83 ⋊ C3×C4 |
| Hall | Dic19 ⋊ C3×C83 |
| Hall | C19⋊C3 ⋊ C4×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C83 | D19⋊C3 |
| commutator, hypocenter | C19 | C3×C4×C83 |
| Frattini | C2 | C83×D19⋊C3 |
| Fitting, socle | C2×C19×C83 | C2×C3 |
| prime radical | C2×C19⋊C3×C83 | C2 |
| cosocle | C2×C19 | C2×C3×C83 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C83 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6308 |
1494 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18924, 11);