Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×SD16×C71 ⋊ C2 |
| Sylow | C71 ⋊ #17910 |
720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|a^2=f,c^2=f,e^2=g,f^2=h,b^a=be,d^a=dgh,e^a=eg,i^a=i^70,e^b=eg,i^d=i^702036 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 139539);