Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C71 ⋊ #1828 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17985860 |
| commutator | C23×C71 | C22×C4 |
| Frattini | C24 | C22×D71 |
| Fitting | C2×#99×C71 | C2 |
| socle | C2×C71 | #381 |
| hypercenter | C2×#99 | D71 |
| hypocenter | C71 | #1828 |
| LCS | G ▷ C23×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C24 ◁ C2×#99 | |
296 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 81 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=f,c^2=d,b^a=bd,c^a=ce,d^a=dg,f^b=fg,e^c=eg,h^c=h^70799 conjugacy classes — view the full character table.
| maximal subgroup of | #31913066, #31913068, #31913071, … |
| maximal normal subgroup of | #31913066, #31913068, #31913071, … |
| maximal quotient of | #31890909, #31890912, #31890915, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4616);