Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C81 · Schur multiplier (H2) = C3 |
| direct product | C3×#15688500 |
| derived, Sylow | C37 ⋊ C3×C81 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C27 | C37⋊C3 |
| commutator, hypocenter | C37 | C3×C81 |
| Frattini | C27 | C3×C37⋊C3 |
| Fitting | C3×C27×C37 | C3 |
| socle | C32×C37 | C27 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C27 | |
36 conjugacy classes of subgroups.
1215 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C81×#66524, C9×#15688500, #41004938, … |
| maximal normal subgroup of | C81×#66524, C9×#15688500, #41004938, … |
| maximal quotient of | C9×#15688500, C32⋊#15688500, #41005050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 125);