Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊C8×C269 ⋊ C2 |
| Sylow | C269 ⋊ C8×D4 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=e,c^2=e,e^2=f,b^a=bd,g^b=g^268,g^c=g^2682720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46809677, #46809679, #46809682, … |
| maximal normal subgroup of | #46809677, #46809679, #46809682, … |
| maximal quotient of | #46809679, #46809684, #46809691, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 614);