Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C73 ⋊ #1784 |
564 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,73|a^2=f,b^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^27,f^b=fg,h^c=h^72,h^f=h^72392 conjugacy classes — view the full character table.
| maximal subgroup of | #34000694, #34000711, #34004512, … |
| maximal normal subgroup of | #34000694, #34000711, #34004512, … |
| maximal quotient of | #34004090, #34004104, #34004105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20345);