Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C19 ⋊ #413 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=e,c^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^18,e^b=ef202 conjugacy classes — view the full character table.
| maximal subgroup of | #14561757, #14561758, #14561763, … |
| maximal normal subgroup of | #14561757, #14561758, #14561763, … |
| maximal quotient of | #14561949, #14561953, #14561969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 533);