Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #117×C269 ⋊ C2 |
| Sylow | C269 ⋊ #418 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,c^b=cf,d^b=df,g^b=g^2682702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46810853, #46810854, #46811261, … |
| maximal normal subgroup of | #46810853, #46810854, #46811261, … |
| maximal quotient of | #46809275, #46809301, #46809327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 553);