Finite Group DatabasebetaFinite Group Databasebeta| order | 8451 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C9×C313⋊C3 |
| Fitting | C9×C313 ⋊ C3 |
| derived, Sylow | C313 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C313⋊C3 |
| commutator, hypocenter | C313 | C3×C9 |
| Frattini | C3 | C3×C313⋊C3 |
| Fitting | C9×C313 | C3 |
| socle | C3×C313 | C32 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C9 | |
20 conjugacy classes of subgroups.
963 conjugacy classes — view the full character table.
| maximal subgroup of | C27×C313⋊C3, #38761680, #38761681, … |
| maximal normal subgroup of | C27×C313⋊C3, #38761680, #38761681, … |
| maximal quotient of | C9×C313⋊C9, (C3×C313⋊C3)⋊C9, (C313⋊C9)⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8451, 7);