Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×#124×C79 ⋊ C2 |
| Sylow | C79 ⋊ #34229 |
2314 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|a^2=h,b^2=h,c^2=f,e^2=g,b^a=bf,c^a=cg,e^a=ef,d^b=df,i^b=i^78,i^d=i^782272 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 330223);