Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×AΣL(1,𝔽16)×C71 ⋊ C2 |
| Sylow | C71 ⋊ #33348 |
1410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^8,71|a^2=f,b^a=be,e^a=eg,g^a=gh,f^b=fg,d^c=dh,i^d=i^70,f^e=fh956 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 322314);