Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #349×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1321 |
112 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 33 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=d,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=cg,d^b=deg,h^b=h^70,d^c=dg796 conjugacy classes — view the full character table.
| maximal subgroup of | #1321×D71, C2×#22586277, #31906578, … |
| maximal normal subgroup of | #1321×D71, C2×#22586277, #31906578, … |
| maximal quotient of | #31884074, #31884076, #31884078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2447);