Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×M16×C181 ⋊ C2 |
| Sylow | C181 ⋊ #2896 |
772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5792 |
Polycyclic presentation:
2^7,181|a^2=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^180,e^b=eg,h^b=h^1803644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 13030);