Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×#106×C71 ⋊ C2 |
| Sylow | C71 ⋊ #9717 |
468 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|a^2=f,b^2=df,c^2=e,d^2=gh,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,f^b=fh,i^b=i^702018 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 68715);