Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M16×C19 ⋊ C2 |
| Sylow | C19 ⋊ #408 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,e^2=f,b^a=bd,g^a=g^18,c^b=cf,g^b=g^18208 conjugacy classes — view the full character table.
| maximal subgroup of | #14561572, #14563584, #14563597, … |
| maximal normal subgroup of | #14561572, #14563584, #14563597, … |
| maximal quotient of | #14561984, #14561988, #14561992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 517);