Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C32 |
| direct product | C3×#15688509 |
| Fitting | C3×C27×C37 ⋊ C3 |
| Sylow | C37 ⋊ C3×C27⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9 | C3×C37⋊C3 |
| commutator | C3×C37 | C32×C9 |
| Frattini | C9 | C32×C37⋊C3 |
| Fitting | C3×C27×C37 | C3 |
| socle | C32×C37 | C3×C9 |
| hypercenter | C3×C27 | C37⋊C3 |
| hypocenter | C37 | C3×C27⋊C3 |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C3×C9 ◁ C3×C27 | |
120 conjugacy classes of subgroups.
1071 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×#15688509, #41006199, #41006202, … |
| maximal normal subgroup of | C9×#15688509, #41006199, #41006202, … |
| maximal quotient of | C3×#22582462, C9×#15688509, C3×#22582465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 237);