Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C8×C269 ⋊ C2 |
| Sylow | C269 ⋊ #416 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^268,d^b=df,g^b=g^2684316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46810721, #46810722, #46810728, … |
| maximal normal subgroup of | #46810721, #46810722, #46810728, … |
| maximal quotient of | #46809268, #46809294, #46809320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 546);