Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×Q8×C269 ⋊ C2 |
| Sylow | C269 ⋊ #393 |
202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^2682702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809835, #46809840, #46809862, … |
| maximal normal subgroup of | #46809835, #46809840, #46809862, … |
| maximal quotient of | #46809127, #46809144, #46809156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 460);