Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #97×C269 ⋊ C2 |
| Sylow | C269 ⋊ C4×M16 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=e,d^2=f,c^a=cf,g^b=g^268,g^c=g^2682720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809470, #46809472, #46809475, … |
| maximal normal subgroup of | #46809470, #46809472, #46809475, … |
| maximal quotient of | #46809164, #46809173, #46809181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 501);