Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C71 ⋊ #1753 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D71 |
| commutator | C22×C71 | C2×C42 |
| Fitting | C22×M16×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | C22×M16 | D71 |
| hypocenter | C71 | #1753 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C22×M16 | |
348 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 145 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=f,c^2=e,e^2=g,b^a=bd,c^a=cg,h^b=h^701456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31915232, #31915238, #1753×D71, … |
| maximal normal subgroup of | #31915232, #31915238, #1753×D71, … |
| maximal quotient of | #31887930, #31887935, #31887940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4291);