Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#397×C79 ⋊ C2 |
| Sylow | C79 ⋊ #14731 |
2254 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|a^2=ef,d^2=e,b^a=be,c^a=cf,d^a=dh,i^a=i^78,c^b=cg,i^c=i^78,i^d=i^781780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 101115);