Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#14556151 |
| Fitting | C22×Q16×C71 ⋊ C2 |
| Sylow | C71 ⋊ C22×#135 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D71 |
| commutator | C4×C71 | C25 |
| Frattini | C4 | C24×D71 |
| Fitting | C22×Q16×C71 | C2 |
| socle | C23×C71 | C2×D4 |
| hypercenter | C22×Q16 | D71 |
| hypocenter | C71 | C22×#135 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×Q16 | |
1504 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 525 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 | #31913102, #31913123, #31998798, … |
| maximal normal subgroup of | #31913102, #31913123, #31998798, … |
| maximal quotient of | C22×#17985994, C22×#17986036, C22×#17986081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 19239);