Finite Group DatabasebetaFinite Group Databasebeta| order | 10449 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C36 |
| unambiguous semidirect product | (C3×C43⋊C3)⋊H(3,𝔽3) |
| Fitting | C3×H(3,𝔽3)×C43 ⋊ C3 |
| Sylow | C43 ⋊ C32⋊H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C43⋊C3 |
| commutator, socle, cosocle | C32×C43 | C33 |
| Fitting | C3×H(3,𝔽3)×C43 | C3 |
| hypercenter | C3×H(3,𝔽3) | C43⋊C3 |
| hypocenter | C43 | C32⋊H(3,𝔽3) |
| LCS | G ▷ C32×C43 ▷ C43 | |
| UCS | C1 ◁ C32 ◁ C3×H(3,𝔽3) | |
378 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,43|b^a=bd,c^a=ce,f^c=f^36513 conjugacy classes — view the full character table.
| maximal subgroup of | #44532514, #44532515, #44532524, … |
| maximal normal subgroup of | #44532514, #44532515, #44532524, … |
| maximal quotient of | #44532245, #44532270, #44532271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 177);