Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×M16×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1395 |
162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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=g,e^2=g,b^a=bc,c^a=cf,e^a=eg,f^a=fg,h^a=h^27,d^b=dfg,h^b=h^72,d^c=dg,h^d=h^72386 conjugacy classes — view the full character table.
| maximal subgroup of | #34012299, C2×#22625032, #34012306, … |
| maximal normal subgroup of | #34012299, C2×#22625032, #34012306, … |
| maximal quotient of | #34000320, #34000369, #34000373, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19611);