Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C79×#3021 ⋊ C2 |
| Sylow | C79 ⋊ #23990 |
1260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1264 |
Polycyclic presentation:
2^8,79|b^2=e,g^2=h,b^a=be,c^a=cf,d^a=de,g^a=gh,i^a=i^78,c^b=cg,i^b=i^78,e^c=eh,g^c=gh,f^d=fh1171 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 202072);