Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C269 ⋊ M64 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^187,g^b=g^268,g^c=g^2681112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46825994, #46825995, #46826038, … |
| maximal normal subgroup of | #46825994, #46825995, #46826038, … |
| maximal quotient of | #46825993, #46825999, #46826043 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1482);