Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#456×C67 ⋊ C2 |
| Sylow | C67 ⋊ #24417 |
1390 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4288 |
Polycyclic presentation:
2^8,67|a^2=fh,d^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,f^b=fh,i^b=i^66,e^c=eh,f^c=fh,f^d=fh1099 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 207048);