Finite Group DatabasebetaFinite Group Databasebeta| order | 33664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C263 ⋊ #1922 |
186 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8416 |
Polycyclic presentation:
2^7,263|a^2=f,b^2=f,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,e^c=eg,h^c=h^2623706 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33664, 5106);