Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #20555 |
1222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|a^2=f,b^2=g,c^2=f,f^2=h,b^a=be,d^a=de,c^b=ce,i^c=i^78,i^d=i^783256 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 168452);