Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C19 ⋊ #323 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=d,d^2=f,b^a=bc,c^a=ce,g^a=g^18,d^b=de202 conjugacy classes — view the full character table.
| maximal subgroup of | #14561562, #14561563, #14561564, … |
| maximal normal subgroup of | #14561562, #14561563, #14561564, … |
| maximal quotient of | #14561456, #14561461, #14561478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 273);