Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C269 ⋊ #324 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^268,d^b=de2702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46808816, #46808817, #46808818, … |
| maximal normal subgroup of | #46808816, #46808817, #46808818, … |
| maximal quotient of | #46808708, #46808728, #46808825, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 275);