Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C79×#2032 ⋊ C2 |
| Sylow | C79 ⋊ #23474 |
1164 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 205 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=e,b^2=e,d^2=h,b^a=be,c^a=cf,f^a=fh,g^a=gh,c^b=cg,g^b=gh,e^c=eh,i^d=i^78943 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 197008);