Finite Group DatabasebetaFinite Group Databasebeta| order | 8451 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C313 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C313⋊C3 |
| commutator, socle | C3×C313 | C32 |
| Fitting | C32×C313 | C3 |
| hypercenter | C32 | C313⋊C3 |
| hypocenter | C313 | 3−1+2 |
| LCS | G ▷ C3×C313 ▷ C313 | |
| UCS | C1 ◁ C3 ◁ C32 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,313|a^3=c,b^a=bc,d^a=d^214947 conjugacy classes — view the full character table.
| maximal subgroup of | #38761683, #38761684, #38761685, … |
| maximal normal subgroup of | #38761683, #38761684, #38761685, … |
| maximal quotient of | C32⋊(C313⋊C9), (C313⋊C9)⋊C9, C3×#22554835 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8451, 12);