Finite Group DatabasebetaFinite Group Databasebeta| order | 6129 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C227 · Schur multiplier (H2) = C1 |
| direct product | 3−1+2×C227 |
| unambiguous semidirect product | C9⋊(C3×C227) |
| unambiguous semidirect product | (C9×C227)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C227 | C32 |
| commutator, Frattini | C3 | C32×C227 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C227 ◁ G | |
16 conjugacy classes of subgroups.
2497 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽27)×C227, #731×C227, #733×C227, … |
| maximal normal subgroup of | AΣL(1,𝔽27)×C227, #731×C227, #733×C227, … |
| maximal quotient of | C32⋊C9×C227, C9⋊C9×C227, C3×3−1+2×C227 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6129, 4);