Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #10597266⋊C3 |
| Fitting | C4⋊C4×C19 ⋊ C2×C3 |
| Hall | #10597266 ⋊ C3 |
| Hall | C19⋊C3 ⋊ #102 |
| Sylow | C19 ⋊ C3×#102 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^2,3,2^3,19|b^2=d,e^2=f,b^a=be,e^a=ef,g^a=g^18,e^b=ef,g^c=g^1172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 19);