Finite Group DatabasebetaFinite Group Databasebeta| order | 5157 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C191 · Schur multiplier (H2) = C32 |
| direct product | H(3,𝔽3)×C191 |
| unambiguous semidirect product | C32⋊(C3×C191) |
| unambiguous semidirect product | (C32×C191)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C191 | C32 |
| commutator, Frattini | C3 | C32×C191 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C191 ◁ G | |
22 conjugacy classes of subgroups.
2101 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽27)×C191, #731×C191, #732×C191, … |
| maximal normal subgroup of | AΣL(1,𝔽27)×C191, #731×C191, #732×C191, … |
| maximal quotient of | C32⋊C9×C191, AΣL(1,𝔽27)×C191, #731×C191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5157, 3);