Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #444×D71 |
| Fitting | #444×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#444 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D71 |
| commutator | C4×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #444×C71 | C2 |
| socle | C2×C71 | C2×C4×D4 |
| hypercenter | #444 | D71 |
| hypocenter | C71 | C2×#444 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C4 ◁ C2×C8 ◁ #444 | |
464 conjugacy classes of subgroups.
814 conjugacy classes — view the full character table.
| maximal subgroup of | #2180×D71, AGL(1,ℤ/16)×D71, #32150897, … |
| maximal normal subgroup of | #2180×D71, AGL(1,ℤ/16)×D71, #32150897, … |
| maximal quotient of | SD16⋊C8×D71, #1579×D71, #1580×D71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13402);