Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×AGL(1,ℤ/8)×C71 ⋊ C2 |
| Sylow | C71 ⋊ #23588 |
1106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|b^2=h,d^2=e,f^2=h,b^a=be,c^a=cf,f^a=fh,g^a=gh,c^b=cg,f^b=fh,i^b=i^70,f^c=fh1592 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 197994);