Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q32×C79 ⋊ C2 |
| Sylow | C79 ⋊ #33853 |
696 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|b^2=h,c^2=h,d^2=h,e^2=gh,g^2=h,b^a=be,c^a=cf,d^a=dgh,e^a=eg,g^a=gh,i^a=i^78,d^b=de,e^b=eg,g^b=gh,i^c=i^78,e^d=eg,g^d=gh1771 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 326305);