Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #336×C73 ⋊ C2 |
| Sylow | C73 ⋊ #1880 |
374 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 103 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,c^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^b=dg,e^b=eg,f^b=fg,h^b=h^72,d^c=dg,e^c=eg,f^c=fg,h^c=h^721478 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1880×D73, C2×#22610285, #33087328, … |
| maximal normal subgroup of | #1880×D73, C2×#22610285, #33087328, … |
| maximal quotient of | #32980565, #32980593, #32980751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 4864);