Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C79×#1560 ⋊ C2 |
| Sylow | C79 ⋊ #18528 |
1060 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 167 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,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,i^a=i^78,e^b=eg,f^b=fh,e^c=eh,f^c=fh,i^c=i^781054 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 145668);