Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | AΣL(1,𝔽16)×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2199 |
270 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|b^a=bd,c^a=ce,f^a=fg,h^a=h^70,c^b=cg,e^b=efg,d^c=df,h^c=h^70,e^d=eg472 conjugacy classes — view the full character table.
| maximal subgroup of | #2199×D71, C2×#22590342, #32151500, … |
| maximal normal subgroup of | #2199×D71, C2×#22590342, #32151500, … |
| maximal quotient of | #31909500, #31909501, #31909540, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6512);