Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C269 ⋊ #419 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=e,b^2=f,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^268,c^b=cf,d^b=df2702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46810857, #46810860, #46811256, … |
| maximal normal subgroup of | #46810857, #46810860, #46811256, … |
| maximal quotient of | #46809280, #46809306, #46809332, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 558);