Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C269 ⋊ #428 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,g^a=g^268,c^b=cf2702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46811096, #46811097, #46811101, … |
| maximal normal subgroup of | #46811096, #46811097, #46811101, … |
| maximal quotient of | #46809637, #46809652, #46809670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 591);