Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10597274⋊C3 |
| Hall | #10597274 ⋊ C3 |
| Hall | C19⋊C3 ⋊ #106 |
| Sylow | C19 ⋊ C3×#106 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^2,3,2^3,19|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,g^a=g^18,g^c=g^1190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 26);