Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C8×C269 ⋊ C4 |
| Sylow | C269 ⋊ #405 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=e,d^2=f,c^b=cf,g^b=g^187,g^e=g^2681112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46825934, #46825937, #46825938, … |
| maximal normal subgroup of | #46825934, #46825937, #46825938, … |
| maximal quotient of | C8×#16864411, C8×#16864412, #46826088, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1512);