Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#365×C79 ⋊ C2 |
| Sylow | C79 ⋊ #33638 |
514 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2528 |
Polycyclic presentation:
2^8,79|a^2=eg,b^2=e,e^2=h,f^2=g,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fg,g^a=gh,d^b=dh,i^b=i^78,f^c=fgh,g^c=gh,i^c=i^781288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 324317);