Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×#14556115 |
| Sylow | C71 ⋊ C22×#124 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D71 |
| commutator | C22×C71 | C25 |
| Frattini | C22 | C24×D71 |
| Fitting | C23×D4×C71 | C2 |
| socle | C24×C71 | C23 |
| hypercenter | C23×D4 | D71 |
| hypocenter | C71 | C22×#124 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 645 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31890064, #31903992, #31903998, … |
| maximal normal subgroup of | #31890064, #31903992, #31903998, … |
| maximal quotient of | C22×#17985864, C22×#17985893, C22×#17985902, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17757);