Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C79×#1822 ⋊ C2 |
| Sylow | C79 ⋊ #20729 |
1382 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 251 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2528 |
Polycyclic presentation:
2^8,79|a^2=g,d^2=e,g^2=h,b^a=be,c^a=cf,f^a=fh,d^b=dh,g^c=gh,i^c=i^78,i^d=i^781306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 169543);