Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C19 ⋊ #108 |
| Sylow | C19 ⋊ #822 |
| Sylow | C3 ⋊ #10597279 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 912 |
Polycyclic presentation:
2^5,3,19|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bd,f^a=f^2,g^a=g^18,d^b=de294 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 243);