Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | #492×D71 |
| Fitting | #492×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#492 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D71 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #492×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #492 | D71 |
| hypocenter | C71 | C2×#492 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #492 | |
656 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
814 conjugacy classes — view the full character table.
| maximal subgroup of | #1359×D71, #1409×D71, #1410×D71, … |
| maximal normal subgroup of | #1359×D71, #1409×D71, #1410×D71, … |
| maximal quotient of | #1705×D71, #1706×D71, #1707×D71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 14914);