Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C19 ⋊ #381 |
218 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=f,c^2=d,b^a=bd,c^a=ce,g^c=g^18208 conjugacy classes — view the full character table.
| maximal subgroup of | #14561564, #14563551, #14563711, … |
| maximal normal subgroup of | #14561564, #14563551, #14563711, … |
| maximal quotient of | #14561857, #14561859, #14561882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 410);