Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×#554×C67 ⋊ C2 |
| Sylow | C67 ⋊ #25946 |
1176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8576 |
Polycyclic presentation:
2^8,67|a^2=eh,b^2=eh,c^2=ef,d^2=eh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,g^a=gh,c^b=cg,f^b=fh,g^b=gh,d^c=dh,i^c=i^661696 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 226585);