Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1803 ⋊ C2 |
| Sylow | C79 ⋊ #24715 |
738 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|a^2=ef,c^2=h,d^2=eh,f^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^78,c^b=cg,d^b=dh,i^b=i^78,f^c=fh1528 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 210954);