Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #123×C73 ⋊ C4 |
| Sylow | C73 ⋊ #1890 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17989535 |
| commutator | C23×C73 | C22×C4 |
| Frattini | C23 | C22×#64408 |
| Fitting | #123×C73 | C4 |
| socle | C2×C73 | #386 |
| hypercenter | #123 | #64408 |
| hypocenter | C73 | #1890 |
| LCS | G ▷ C23×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #123 | |
386 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 68 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=f,b^2=dfg,b^a=bd,c^a=ce,e^a=eg,h^a=h^46,e^b=eg,h^b=h^27,d^c=dg,f^c=fg,h^f=h^72284 conjugacy classes — view the full character table.
| maximal subgroup of | #34012958, #34012959, #34012960, … |
| maximal normal subgroup of | #34012958, #34012959, #34012960, … |
| maximal quotient of | #34005892, #34005893, #34005894, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20520);