Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C19×#100 ⋊ C2 |
| Sylow | C19 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 152 |
Polycyclic presentation:
2^6,19|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^18,d^b=de,g^b=g^18,d^c=df112 conjugacy classes — view the full character table.
| maximal subgroup of | D19×AΣL(1,𝔽16), C2×#11926332, #14565275, … |
| maximal normal subgroup of | D19×AΣL(1,𝔽16), C2×#11926332, #14565275, … |
| maximal quotient of | #14561562, #14561584, #14561633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 337);