Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #1278 |
172 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 62 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=d,b^2=e,c^2=f,d^2=g,e^2=g,b^a=bc,c^a=cf,e^a=ef,h^b=h^27,h^e=h^72416 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22624762, #34002094, #34002099, … |
| maximal normal subgroup of | C2×#22624762, #34002094, #34002099, … |
| maximal quotient of | #33999891, #33999903, #33999909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19341);