Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#17986416 |
| Sylow | C71 ⋊ C2×#504 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D71 |
| commutator | C2×C71 | C23×C8 |
| Frattini | C8 | C23×D71 |
| Fitting | C2×#131×C71 | C2 |
| socle | C22×C71 | C22×C8 |
| hypercenter | C2×#131 | D71 |
| hypocenter | C71 | C2×#504 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C8 ◁ C2×#131 | |
368 conjugacy classes of subgroups.
1480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31912550, #31912551, #31912556, … |
| maximal normal subgroup of | #31912550, #31912551, #31912556, … |
| maximal quotient of | C2×#22589937, C4×#17986416, C2×#22589954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17609);