Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Fitting | C4×#117×C79 ⋊ C2 |
| Sylow | C79 ⋊ #21212 |
1658 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|a^2=g,b^2=eg,c^2=f,d^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^78,e^b=eh,g^b=gh3184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 173317);