Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊Q8×C269 ⋊ C2 |
| Sylow | C269 ⋊ #456 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,g^b=g^268,d^c=df1892 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809038, #46809040, #46812906, … |
| maximal normal subgroup of | #46809038, #46809040, #46812906, … |
| maximal quotient of | #46809846, #46809853, #46809858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 731);