Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C19 ⋊ #482 |
106 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 39 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|b^2=f,c^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^18145 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#482, C2×#11926865, #14573544, … |
| maximal normal subgroup of | D19×#482, C2×#11926865, #14573544, … |
| maximal quotient of | #14563727, #14563832, #14563958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 870);