Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C269 ⋊ C8×Q8 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,g^c=g^2682720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809684, #46809688, #46809689, … |
| maximal normal subgroup of | #46809684, #46809688, #46809689, … |
| maximal quotient of | #46810746, #46810750, #46811439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 673);