Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C73 ⋊ #1585 |
168 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 54 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=e,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^27,d^b=df,h^b=h^72,h^c=h^27,h^e=h^72290 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22625547, D73⋊#1585, #34018376, … |
| maximal normal subgroup of | C2×#22625547, D73⋊#1585, #34018376, … |
| maximal quotient of | #34003664, #34003699, #34004040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20126);