Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C23×(C2×D71)⋊C4 |
| Fitting | C24×C4×C71 ⋊ C2 |
| Sylow | C71 ⋊ C23×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D71 |
| commutator | C2×C71 | C24×C4 |
| Frattini | C22 | C24×D71 |
| Fitting | C24×C4×C71 | C2 |
| socle | C25×C71 | C22 |
| hypercenter | C24×C4 | D71 |
| hypocenter | C71 | C23×C22⋊C4 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
4632 conjugacy classes of subgroups; only the 1413 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1413 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31885373, #31888778, C2×(C2×D71)⋊#95, … |
| maximal normal subgroup of | #31885373, #31888778, C2×(C2×D71)⋊#95, … |
| maximal quotient of | C23×C71⋊#95, C22×C4×(C2×D71)⋊C4, C22×#17985854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17667);