Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ #1570 |
168 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 89 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=e,b^2=d,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cg,h^b=h^701438 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31891475, #31891476, #31891480, … |
| maximal normal subgroup of | #31891475, #31891476, #31891480, … |
| maximal quotient of | #31886927, #31888660, #31890298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 3280);