Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C42×C269 ⋊ C4 |
| Sylow | C269 ⋊ #354 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=f,c^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^187,c^b=cf,d^b=def,g^b=g^268,d^c=df,g^d=g^2681085 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46826012, #46826013, #46826014, … |
| maximal normal subgroup of | #46826012, #46826013, #46826014, … |
| maximal quotient of | #46825816, #46825825, #46825866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1456);