Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q64×D71 |
| Fitting | Q64×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×Q64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D71 |
| commutator | C16×C71 | C23 |
| Frattini | C16 | C22×D71 |
| Fitting | Q64×C71 | C2 |
| socle | C2×C71 | C2×D16 |
| hypercenter | Q64 | D71 |
| hypocenter | C71 | C2×Q64 |
| LCS | G ▷ C16×C71 ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64 | |
104 conjugacy classes of subgroups.
703 conjugacy classes — view the full character table.
| maximal subgroup of | SD128×D71, Q128×D71, #31918513, … |
| maximal normal subgroup of | SD128×D71, Q128×D71, #31918513, … |
| maximal quotient of | #1416×D71, #1423×D71, #31918035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6813);