Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #21119 |
858 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20224 |
Polycyclic presentation:
2^8,79|a^2=g,b^2=gh,c^2=h,d^2=e,f^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^78,i^b=i^78,f^c=fh2260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 172564);