Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C71 ⋊ #1716 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14556124 |
| commutator | C42×C71 | C23 |
| Frattini | C42 | C22×D71 |
| Fitting | #494×C71 | C2 |
| socle | C22×C71 | #127 |
| hypercenter | #494 | D71 |
| hypocenter | C71 | #1716 |
| LCS | G ▷ C42×C71 ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #494 | |
176 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=f,b^2=df,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,h^c=h^70796 conjugacy classes — view the full character table.
| maximal subgroup of | #31885320, #31885322, #31911226, … |
| maximal normal subgroup of | #31885320, #31885322, #31911226, … |
| maximal quotient of | #31891238, #31897221, #31897235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4141);