Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C269 ⋊ #442 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=e,c^2=ef,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^268,d^b=df,g^c=g^2681898 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46812784, #46812786, #442×D269, … |
| maximal normal subgroup of | #46812784, #46812786, #442×D269, … |
| maximal quotient of | #46809709, #46809750, #46809799, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 661);