Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C71 ⋊ #2955 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D71 |
| commutator | C4×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #575×C71 | C2 |
| socle | C2×C71 | C2×C4×D4 |
| hypercenter | #575 | D71 |
| hypocenter | C71 | #2955 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^70,e^b=eg,h^c=h^70814 conjugacy classes — view the full character table.
| maximal subgroup of | #32003415, #32003417, #32003426, … |
| maximal normal subgroup of | #32003415, #32003417, #32003426, … |
| maximal quotient of | AGL(1,ℤ/8)×C71⋊C8, #137×C71⋊C8, #31967037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13413);