Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C4×#41×C73 ⋊ C2 |
| Sylow | C73 ⋊ #3498 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D73 |
| commutator, socle | C22×C73 | C25 |
| Fitting | C4×#41×C73 | C2 |
| hypercenter | C4×#41 | D73 |
| hypocenter | C73 | #3498 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
1748 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1748 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,73|c^2=g,e^2=f,b^a=bf,c^a=cg,e^a=ef,h^a=h^72,d^b=df1484 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32977892, #32977896, #32978200, … |
| maximal normal subgroup of | #32977892, #32977896, #32978200, … |
| maximal quotient of | #33246088, #33246361, #33246389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 18288);