Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C8×C22⋊C4×C67 ⋊ C2 |
| Sylow | C67 ⋊ #20562 |
1002 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8576 |
Polycyclic presentation:
2^8,67|a^2=f,b^2=g,c^2=f,f^2=h,b^a=be,d^a=de,c^b=ceh,d^b=dh,i^b=i^66,i^d=i^662740 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 168537);