Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M64×C181 ⋊ C2 |
| Sylow | C181 ⋊ #2258 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11584 |
Polycyclic presentation:
2^7,181|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^180,c^b=cg,h^c=h^1803680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 6805);