Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#14556160 |
| Fitting | C22×Q16×C71 ⋊ C2 |
| Sylow | C71 ⋊ C22×#137 |
| 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×#137 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×Q16 | |
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 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.
1024 conjugacy classes — view the full character table.
| maximal subgroup of | #31998816, #31998827, #31998852, … |
| maximal normal subgroup of | #31998816, #31998827, #31998852, … |
| maximal quotient of | C22×#17986006, C22×#17985999, C22×#17986040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 19250);