Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | Q8×#41×C79 ⋊ C2 |
| Sylow | C79 ⋊ #61470 |
1812 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|a^2=h,b^2=h,c^2=h,e^2=f,g^2=h,b^a=bf,c^a=cg,d^a=dh,e^a=eh,g^a=gh,i^a=i^78,c^b=ch,d^b=df,g^c=gh2005 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 1051932);