Finite Group DatabasebetaFinite Group Databasebeta| order | 7857 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C34 |
| direct product | H(3,𝔽3)×C97⋊C3 |
| Fitting | H(3,𝔽3)×C97 ⋊ C3 |
| Sylow | C97 ⋊ C3×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×C97⋊C3 |
| commutator, socle | C3×C97 | C33 |
| Fitting | H(3,𝔽3)×C97 | C3 |
| hypercenter | H(3,𝔽3) | C97⋊C3 |
| hypocenter | C97 | C3×H(3,𝔽3) |
| LCS | G ▷ C3×C97 ▷ C97 | |
| UCS | C1 ◁ C3 ◁ H(3,𝔽3) | |
112 conjugacy classes of subgroups.
385 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽27)×C97⋊C3, #731×C97⋊C3, #732×C97⋊C3, … |
| maximal normal subgroup of | AΣL(1,𝔽27)×C97⋊C3, #731×C97⋊C3, #732×C97⋊C3, … |
| maximal quotient of | C32⋊C9×C97⋊C3, #37555860, H(3,𝔽3)×C97⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7857, 40);