Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | #126×Dic71 |
| Sylow | C71 ⋊ C4×#126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator | C22×C71 | C23×C4 |
| Fitting | C2×#126×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C2×#126 | D71 |
| hypocenter | C71 | C4×#126 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×#126 | |
516 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1036 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#126×D71, C2×#126×Dic71, C4×#17986532, … |
| maximal normal subgroup of | C4×#126×D71, C2×#126×Dic71, C4×#17986532, … |
| maximal quotient of | #388×Dic71, #387×Dic71, #383×Dic71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7062);