Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C71 ⋊ #2103 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14556116 |
| commutator | C22×C4×C71 | C23 |
| Frattini | C22×C4 | C22×D71 |
| Fitting | #338×C71 | C2 |
| socle | C2×C71 | #400 |
| hypercenter | #338 | D71 |
| hypocenter | C71 | #2103 |
| LCS | G ▷ C22×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #338 | |
148 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,71|a^2=d,b^2=de,c^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^b=h^70,h^c=h^70796 conjugacy classes — view the full character table.
| maximal subgroup of | #31910812, #31910817, #31910823, … |
| maximal normal subgroup of | #31910812, #31910817, #31910823, … |
| maximal quotient of | #31902578, #31902583, #31902588, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6091);