Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C269 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2152 |
Polycyclic presentation:
2^6,269|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^268,d^b=de,d^c=df1889 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽16)×D269, C2×#31770392, #46812523, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D269, C2×#31770392, #46812523, … |
| maximal quotient of | #46808813, #46808833, #46808882, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 336);