Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#17985916 |
| Fitting | C22×C4⋊C4×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#394 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D71 |
| commutator | C23×C71 | C24 |
| Frattini | C23 | C23×D71 |
| Fitting | C22×C4⋊C4×C71 | C2 |
| socle | C24×C71 | C23 |
| hypercenter | C22×C4⋊C4 | D71 |
| hypocenter | C71 | C2×#394 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
1252 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 261 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31892464, #31892466, #31892469, … |
| maximal normal subgroup of | #31892464, #31892466, #31892469, … |
| maximal quotient of | C2×#22586580, C2×#22586582, C2×#22586588, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7716);