Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M32×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2117 |
220 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 220 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,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^70,d^b=dg,e^b=eg,h^b=h^701444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31912525, #31912529, #31912576, … |
| maximal normal subgroup of | #31912525, #31912529, #31912576, … |
| maximal quotient of | #31906523, #31906526, #31906595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6139);