Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C269 ⋊ #376 |
178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=e,b^2=f,c^2=d,b^a=bd,g^b=g^2684328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46808713, #46808777, #46808779, … |
| maximal normal subgroup of | #46808713, #46808777, #46808779, … |
| maximal quotient of | C4×#22575360, #46809110, #46809112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 395);