Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C269 ⋊ #491 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=f,b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,c^b=cf,g^c=g^2681892 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #491×D269, C2×#31770972, #46821227, … |
| maximal normal subgroup of | #491×D269, C2×#31770972, #46821227, … |
| maximal quotient of | #46811017, #46811572, #46811573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 916);