Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C79 ⋊ #17618 |
1202 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 395 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=f,c^2=gh,d^2=gh,e^2=h,b^a=be,e^a=eg,i^a=i^78,e^b=eh,f^b=fgh,d^c=dgh1777 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 137315);