Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C269 ⋊ H(3,ℤ/4) |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=e,c^2=f,b^a=bc,e^a=ef,g^a=g^268,d^b=df,g^b=g^2682702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46808870, #46808871, #46808873, … |
| maximal normal subgroup of | #46808870, #46808871, #46808873, … |
| maximal quotient of | #46808713, #46808716, #46808739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 306);