Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | #379×D71 |
| Fitting | #379×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator | C22×C71 | C23×C4 |
| Fitting | #379×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | #379 | D71 |
| hypocenter | C71 | C2×#379 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #379 | |
3464 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 365 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 | #1304×D71, #31887775, #1316×D71, … |
| maximal normal subgroup of | #1304×D71, #31887775, #1316×D71, … |
| maximal quotient of | C22⋊#95×D71, #31918657, #379×Dic71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6876);