Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C71×#1511 ⋊ C2 |
| Sylow | C71 ⋊ #18134 |
1202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,i^a=i^70,e^b=eg,f^b=fh,i^b=i^70,e^c=eh,i^c=i^70947 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 141957);