Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | D4×M16×C79 ⋊ C2 |
| Sylow | C79 ⋊ #60141 |
2862 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2528 |
Polycyclic presentation:
2^8,79|a^2=g,c^2=g,g^2=h,b^a=bf,e^a=eh,d^c=dh,i^d=i^78,i^e=i^782038 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 1033492);