Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C8×C269 ⋊ C2 |
| Sylow | C269 ⋊ #448 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|b^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^268,d^b=df,g^b=g^2682699 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809838, #46809839, #46809850, … |
| maximal normal subgroup of | #46809838, #46809839, #46809850, … |
| maximal quotient of | #46809810, #46809827, #46809878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 690);