Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ #2082 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17985926 |
| commutator | C22×C4×C71 | C23 |
| Frattini | C22×C4 | C22×D71 |
| Fitting | #344×C71 | C2 |
| socle | C2×C71 | #397 |
| hypercenter | #344 | D71 |
| hypocenter | C71 | #2082 |
| LCS | G ▷ C22×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #344 | |
184 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 59 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=g,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,h^b=h^70,e^c=eg,f^c=fg,h^c=h^70793 conjugacy classes — view the full character table.
| maximal subgroup of | #2082×D71, C2×#22589806, #32026401, … |
| maximal normal subgroup of | #2082×D71, C2×#22589806, #32026401, … |
| maximal quotient of | #31902247, #31902252, #31902264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5976);