Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C19×#97 ⋊ C2 |
| Sylow | C19 ⋊ #329 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=d,c^2=f,d^2=e,b^a=bc,c^a=ce,c^b=cf,d^b=def,g^b=g^18199 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#329, C2×#11926283, #14562221, … |
| maximal normal subgroup of | D19×#329, C2×#11926283, #14562221, … |
| maximal quotient of | #14561455, #14561460, #14561517, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 288);