Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×Q16×C19 ⋊ C2 |
| Hall | C3×C19 ⋊ SD32 |
| Sylow | C19 ⋊ #828 |
| Sylow | C3 ⋊ #10597285 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 912 |
Polycyclic presentation:
2^5,3,19|b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=g^18,c^b=cd,d^b=de207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 249);