Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C269 ⋊ #405 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=e,d^2=f,c^b=cf,g^b=g^2684328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46808970, #46808972, #46808973, … |
| maximal normal subgroup of | #46808970, #46808972, #46808973, … |
| maximal quotient of | C8×#16864386, #46809168, #46809174, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 504);