Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×B(4,𝔽2)×C89 ⋊ C2 |
| Sylow | C89 ⋊ #23996 |
1396 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1424 |
Polycyclic presentation:
2^8,89|b^2=e,b^a=be,c^a=cf,d^a=de,g^a=gh,i^a=i^88,c^b=cg,g^b=gh,i^b=i^88,e^c=eh,f^d=fh1448 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 202138);