Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C79×#3204 ⋊ C2 |
| Sylow | C79 ⋊ #60749 |
2166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|e^2=h,g^2=h,b^a=bf,c^a=cg,d^a=df,g^a=gh,c^b=cf,d^b=dh,i^b=i^78,g^c=gh,i^c=i^78,i^d=i^78,i^e=i^781066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 1040299);