Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C19×M32 ⋊ C2 |
| Sylow | C19 ⋊ #349 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,d^b=df,g^b=g^18202 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#349, C2×#11926325, #14565254, … |
| maximal normal subgroup of | D19×#349, C2×#11926325, #14565254, … |
| maximal quotient of | #14561558, #14561574, #14561592, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 330);