Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #107×C269 ⋊ C2 |
| 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,c^b=cf,g^b=g^268,g^c=g^2681898 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #428×D269, C2×#31770646, #46819472, … |
| maximal normal subgroup of | #428×D269, C2×#31770646, #46819472, … |
| maximal quotient of | #46809636, #46809651, #46809669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 590);