Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#100×C251 ⋊ C2 |
| Sylow | C251 ⋊ #1903 |
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4016 |
Polycyclic presentation:
2^7,251|a^2=f,b^2=dfg,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^250,e^b=eg,h^b=h^250,d^c=dg,e^c=eg,f^c=fg,h^c=h^2502779 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 4993);