Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C4×C19 ⋊ C22 |
| Hall | C3×C19 ⋊ C2×C22⋊C4 |
| Sylow | C19 ⋊ D3×C22⋊C4 |
| Sylow | C3 ⋊ C22⋊C4×D19 |
264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 456 |
Polycyclic presentation:
2^5,3,19|c^2=d,c^a=ce,g^a=g^18,c^b=ce,f^b=f^2192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 617);