Finite Group DatabasebetaFinite Group Databasebeta| order | 10449 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27 · Schur multiplier (H2) = C33 |
| direct product | C32×C43⋊C27 |
| derived, Sylow | C43 ⋊ C32×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C9 | C43⋊C3 |
| commutator, hypocenter | C43 | C32×C27 |
| Frattini | C9 | C32×C43⋊C3 |
| Fitting | C32×C9×C43 | C3 |
| socle, prime radical | C33×C43 | C9 |
| cosocle | C9×C43 | C33 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C32×C9 | |
144 conjugacy classes of subgroups.
1377 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44531893, H(3,𝔽3)⋊(C43⋊C27), #44531896, … |
| maximal normal subgroup of | #44531893, H(3,𝔽3)⋊(C43⋊C27), #44531896, … |
| maximal quotient of | C3×C9×C43⋊C27, C3×C32⋊(C43⋊C27), C3×#23782733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 235);