Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C4⋊C8×C269 ⋊ C2 |
| Sylow | C269 ⋊ #433 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=e,c^2=d,e^2=f,b^a=bd,c^b=cf,g^b=g^268,g^c=g^2682708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #433×D269, C2×#31770665, #46819519, … |
| maximal normal subgroup of | #433×D269, C2×#31770665, #46819519, … |
| maximal quotient of | #46810635, #46810650, #46810744, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 609);