Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C35 |
| direct product | C32×#11758606 |
| Fitting | C32×C9×C37 ⋊ C3 |
| Sylow | C37 ⋊ C32×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center | C33 | C3×C37⋊C3 |
| commutator | C3×C37 | C34 |
| Frattini | C3 | C33×C37⋊C3 |
| Fitting | C32×C9×C37 | C3 |
| socle | C33×C37 | C32 |
| hypercenter | C32×C9 | C37⋊C3 |
| hypocenter | C37 | C32×3−1+2 |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C33 ◁ C32×C9 | |
576 conjugacy classes of subgroups.
1071 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #41004959, #41005143, #41005162, … |
| maximal normal subgroup of | #41004959, #41005143, #41005162, … |
| maximal quotient of | C32×#15688502, C32×#15688504, C32×#15688506, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 297);