Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C71×#2242 ⋊ C2 |
| Sylow | C71 ⋊ #33702 |
602 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|b^2=f,c^2=e,e^2=gh,f^2=g,g^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fgh,g^a=gh,d^b=dh,i^b=i^70,i^d=i^701382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 324899);