Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C19×C4⋊C8 ⋊ C2 |
| Sylow | C19 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,c^b=ce,g^b=g^18208 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D4⋊C8, C2×#11926271, #14562015, … |
| maximal normal subgroup of | D19×D4⋊C8, C2×#11926271, #14562015, … |
| maximal quotient of | #14561455, #14561459, #14561474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 276);