Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C8×C269 ⋊ C2 |
| Sylow | C269 ⋊ #478 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^268,e^c=ef,g^c=g^2682699 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #478×D269, C2×#31770906, #46820672, … |
| maximal normal subgroup of | #478×D269, C2×#31770906, #46820672, … |
| maximal quotient of | #46810896, #46811135, #46811149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 850);