Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #543×D71 |
| Fitting | #543×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#543 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D71 |
| commutator, socle | C22×C71 | C25 |
| Fitting | #543×C71 | C2 |
| hypercenter | #543 | D71 |
| hypocenter | C71 | C2×#543 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #543 | |
1296 conjugacy classes of subgroups; only the 517 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 517 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 | #1596×D71, #1602×D71, #1608×D71, … |
| maximal normal subgroup of | #1596×D71, #1602×D71, #1608×D71, … |
| maximal quotient of | #2315×D71, #2329×D71, #32156603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17903);