Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C3×#15688505 |
| Sylow | C37 ⋊ C3×C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center | C33 | C3×C37⋊C3 |
| commutator | C3×C37 | C32×C9 |
| Frattini | C32 | C32×C37⋊C3 |
| Fitting | C32×C9×C37 | C3 |
| socle | C33×C37 | C32 |
| hypercenter | C32×C9 | C37⋊C3 |
| hypocenter | C37 | C3×C9⋊C9 |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C33 ◁ C32×C9 | |
180 conjugacy classes of subgroups.
1071 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #41004814, #41004815, #41004988, … |
| maximal normal subgroup of | #41004814, #41004815, #41004988, … |
| maximal quotient of | C3×#22582441, C9×#15688505, #41005102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 161);