Finite Group DatabasebetaFinite Group Databasebeta| order | 8991 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C32 |
| direct product | 3−1+2×#66524 |
| Sylow | C37 ⋊ C9×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C37⋊C3 |
| commutator | C3×C37 | C32×C9 |
| Fitting | C3×3−1+2×C37 | C3 |
| socle | C32×C37 | C33 |
| hypercenter | C3×3−1+2 | C37⋊C3 |
| hypocenter | C37 | C9×3−1+2 |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C32 ◁ C3×3−1+2 | |
148 conjugacy classes of subgroups.
495 conjugacy classes — view the full character table.
| maximal subgroup of | #41005292, #41005294, #41005296, … |
| maximal normal subgroup of | #41005292, #41005294, #41005296, … |
| maximal quotient of | C32⋊C9×#66524, C9⋊C9×#66524, #41005132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8991, 175);