Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D73⋊#338 |
| Sylow | C73 ⋊ C2×#338 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×C4×#64408 |
| commutator | C4×C73 | C2×C42 |
| Frattini | C2×C4 | C22×#64408 |
| Fitting | C2×M16×C73 | C4 |
| socle | C2×C73 | C2×#95 |
| hypercenter | C2×M16 | #64408 |
| hypocenter | C73 | C2×#338 |
| LCS | G ▷ C4×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
372 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 128 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,b^2=f,d^2=g,e^2=g,f^2=g,b^a=bd,f^a=fg,h^a=h^27,e^b=eg,h^c=h^72,h^e=h^72404 conjugacy classes — view the full character table.
| maximal subgroup of | #34000538, #34000546, #338×#64408, … |
| maximal normal subgroup of | #34000538, #34000546, #338×#64408, … |
| maximal quotient of | #34002002, #34002004, #34002006, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20184);