Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C19 ⋊ #365 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,d^b=df,g^b=g^18142 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#365, C2×#11926366, #14565406, … |
| maximal normal subgroup of | D19×#365, C2×#11926366, #14565406, … |
| maximal quotient of | #14561700, #14561733, C2×#11926366 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 371);