Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C79×#1768 ⋊ C2 |
| Sylow | C79 ⋊ #29134 |
690 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|a^2=fg,b^2=gh,d^2=e,f^2=h,b^a=be,c^a=cf,d^a=de,c^b=cg,d^b=dh,f^c=fh,i^c=i^782230 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 269333);