Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C71×#1831 ⋊ C2 |
| Sylow | C71 ⋊ #7659 |
566 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|a^2=e,c^2=fg,d^2=g,e^2=h,b^a=bd,d^a=df,i^a=i^70,c^b=ch,d^b=dg,e^b=efg,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, 57925);