Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C4×#126×C71 ⋊ C2 |
| Sylow | C71 ⋊ #34803 |
1812 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|a^2=gh,b^2=g,d^2=g,e^2=f,b^a=bf,c^a=cg,c^b=ch,d^b=dh,i^b=i^70,i^c=i^702036 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 339317);