Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C19×#106 ⋊ C2 |
| Sylow | C19 ⋊ #360 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=d,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cef,d^b=df,e^b=ef,g^b=g^18142 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#360, C2×#11926353, #14565369, … |
| maximal normal subgroup of | D19×#360, C2×#11926353, #14565369, … |
| maximal quotient of | #14561601, #14561604, #14561643, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 358);