Finite Group DatabasebetaFinite Group Databasebeta| order | 8451 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C9×C313 ⋊ C3 |
| Sylow | C313 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C313⋊C3 |
| commutator, socle | C3×C313 | C32 |
| Fitting | C9×C313 | C3 |
| hypercenter | C9 | C313⋊C3 |
| hypocenter | C313 | 3−1+2 |
| LCS | G ▷ C3×C313 ▷ C313 | |
| UCS | C1 ◁ C3 ◁ C9 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,313|a^3=c,b^a=bc,d^b=d^214947 conjugacy classes — view the full character table.
| maximal subgroup of | 3−1+2×C313⋊C3, C3×#22554833, #38761702, … |
| maximal normal subgroup of | 3−1+2×C313⋊C3, C3×#22554833, #38761702, … |
| maximal quotient of | (C3×C313⋊C3)⋊C9, (C313⋊C9)⋊C9, #38761677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8451, 10);