Finite Group DatabasebetaFinite Group Databasebeta| order | 37504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C293 ⋊ #1801 |
272 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 18752 |
Polycyclic presentation:
2^7,293|a^2=f,b^2=d,c^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^138,f^c=fg,h^f=h^2922368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37504, 20376);