Finite Group DatabasebetaFinite Group Databasebeta| order | 22688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C23×C709 ⋊ C4 |
| Sylow | C709 ⋊ #99 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5672 |
Polycyclic presentation:
2^5,709|a^2=d,b^a=bc,c^a=ce,f^a=f^96,d^b=de,f^d=f^7081427 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22688, 204);