Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C89×#1841 ⋊ C2 |
| Sylow | C89 ⋊ #23362 |
706 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2848 |
Polycyclic presentation:
2^8,89|a^2=g,c^2=ef,d^2=eh,f^2=h,b^a=be,c^a=cf,d^a=def,e^a=eh,c^b=cef,d^b=de,f^b=fh,g^b=gh,i^b=i^88,g^c=gh1448 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 196149);