Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C4×#97×C79 ⋊ C2 |
| Sylow | C79 ⋊ #20480 |
1022 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|a^2=f,b^2=g,c^2=f,d^2=e,f^2=h,b^a=be,c^a=ch,d^a=dh,i^a=i^78,d^c=dh3220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 167857);