Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C89 ⋊ #23831 |
682 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22784 |
Polycyclic presentation:
2^8,89|a^2=eh,b^2=e,c^2=h,d^2=ef,g^2=h,b^a=be,c^a=cf,d^a=dh,c^b=cg,g^b=gh,i^b=i^88,g^c=gh,i^c=i^882516 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 200426);