Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C19 ⋊ C4×D4 |
| Sylow | C19 ⋊ C4×#67 |
| Sylow | C3 ⋊ (C22⋊D19)⋊C4 |
188 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 912 |
Polycyclic presentation:
2^5,3,19|c^2=d,b^a=be,g^a=g^18,c^b=ce,f^b=f^2198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 561);