Finite Group DatabasebetaFinite Group Databasebeta| order | 10827 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C401 · Schur multiplier (H2) = C32 |
| direct product | H(3,𝔽3)×C401 |
| unambiguous semidirect product | C32⋊(C3×C401) |
| unambiguous semidirect product | (C32×C401)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C401 | C32 |
| commutator, Frattini, cosocle | C3 | C32×C401 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C401 ◁ G | |
22 conjugacy classes of subgroups.
4411 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽27)×C401, #731×C401, #732×C401, … |
| maximal normal subgroup of | AΣL(1,𝔽27)×C401, #731×C401, #732×C401, … |
| maximal quotient of | C32⋊C9×C401, AΣL(1,𝔽27)×C401, #731×C401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10827, 3);