Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #336×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1876 |
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|a^2=f,b^2=df,d^2=g,e^2=g,b^a=bd,c^a=ce,d^b=dg,e^b=eg,f^b=fg,h^b=h^70,d^c=dg,e^c=eg,f^c=fg,h^c=h^701438 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1876×D71, C2×#22588666, #31998740, … |
| maximal normal subgroup of | #1876×D71, C2×#22588666, #31998740, … |
| maximal quotient of | #31892012, #31892019, #31892026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4836);