Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C19×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C19 ⋊ #472 |
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^b=g^18,e^c=ef115 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#472, C2×#11926812, #14573350, … |
| maximal normal subgroup of | D19×#472, C2×#11926812, #14573350, … |
| maximal quotient of | #14562988, #14562993, #14563032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 817);