Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C19 ⋊ #124 |
| Sylow | C19 ⋊ #947 |
| Sylow | C3 ⋊ #10597321 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 912 |
Polycyclic presentation:
2^5,3,19|a^2=e,b^2=de,c^2=e,b^a=bd,c^a=ce,g^a=g^18,f^b=f^2240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 456);