Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C4×H(5,𝔽2)×C79 ⋊ C2 |
| Sylow | C79 ⋊ #21473 |
1486 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2528 |
Polycyclic presentation:
2^8,79|a^2=g,d^2=g,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^78,e^b=eh,f^b=fh,d^c=dh,e^c=eh2710 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 175486);