Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C19 ⋊ C2 |
| Sylow | C19 ⋊ #385 |
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=f,b^2=f,b^a=bd,c^a=ce,g^c=g^18208 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#385, C2×#11926415, #14566072, … |
| maximal normal subgroup of | D19×#385, C2×#11926415, #14566072, … |
| maximal quotient of | (C2×D19)⋊#95, #14561866, #14561867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 420);