Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C4×C22⋊Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #34849 |
2160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|b^2=g,c^2=gh,e^2=f,b^a=bf,c^a=cg,i^a=i^78,c^b=ch,d^b=dh,i^b=i^782260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 340070);