Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C79×#3290 ⋊ C2 |
| Sylow | C79 ⋊ #33857 |
646 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|a^2=h,e^2=gh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,g^a=gh,c^b=ch,d^b=de,e^b=eg,g^b=gh,i^b=i^78,f^c=fh,e^d=eg,g^d=gh1174 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 326351);