Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | AΣL(1,𝔽16)×C73 ⋊ C2 |
| Sylow | C73 ⋊ #2122 |
266 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 55 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=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,e^b=ef,h^c=h^72,e^d=eg491 conjugacy classes — view the full character table.
| maximal subgroup of | #2122×D73, C2×#22611579, #33238723, … |
| maximal normal subgroup of | #2122×D73, C2×#22611579, #33238723, … |
| maximal quotient of | #32995075, #32995163, #32995241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 6158);