Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #332×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1553 |
242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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,c^2=fg,d^2=g,e^2=fg,b^a=bd,c^a=cf,d^a=df,d^b=dg,e^b=efg,h^b=h^70,h^c=h^70697 conjugacy classes — view the full character table.
| maximal subgroup of | #1553×D71, C2×#22587044, #31965841, … |
| maximal normal subgroup of | #1553×D71, C2×#22587044, #31965841, … |
| maximal quotient of | #31885473, #31885483, #31885591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 3214);