Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | D4×M16×C79 ⋊ C2 |
| Sylow | C79 ⋊ #18001 |
740 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|a^2=f,c^2=fg,e^2=g,f^2=h,b^a=be,c^a=cg,e^a=eg,i^a=i^78,e^b=eg,d^c=dh2008 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 140539);