Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C42 |
No aliases for this group.
| Fitting | C79×#1437 ⋊ C2 |
| Sylow | C79 ⋊ #14358 |
3538 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|a^2=h,b^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,i^b=i^78,i^c=i^782248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 96862);