Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×Q8×C37 ⋊ C4 |
| Sylow | C37 ⋊ #1520 |
288 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^7,37|a^2=e,b^2=f,c^2=g,d^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^31,c^b=cf,d^b=dg,e^b=efg,h^b=h^36,h^c=h^36,h^e=h^36212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 19950);