Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C71×#1390 ⋊ C2 |
| Sylow | C71 ⋊ #12573 |
838 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|a^2=e,b^2=f,c^2=h,b^a=bd,d^a=dg,g^a=gh,e^b=eg,i^c=i^70,e^d=eh962 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 84509);