Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C79×#1779 ⋊ C2 |
| Sylow | C79 ⋊ #23309 |
1026 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 215 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|a^2=g,g^2=h,b^a=be,c^a=cf,d^a=defh,c^b=cefh,d^b=deh,i^b=i^782236 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 195622);