Finite Group DatabasebetaFinite Group Databasebeta| order | 7857 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
| direct product | C3×#14579755 |
| Fitting | C3×C9×C97 ⋊ C3 |
| Sylow | C97 ⋊ C3×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C3×C97⋊C3 |
| commutator | C3×C97 | C33 |
| Frattini | C3 | C32×C97⋊C3 |
| Fitting | C3×C9×C97 | C3 |
| socle | C32×C97 | C32 |
| hypercenter | C3×C9 | C97⋊C3 |
| hypocenter | C97 | C3×3−1+2 |
| LCS | G ▷ C3×C97 ▷ C97 | |
| UCS | C1 ◁ C32 ◁ C3×C9 | |
76 conjugacy classes of subgroups.
897 conjugacy classes — view the full character table.
| maximal subgroup of | #14579755⋊C9, C9×#14579755, #37555873, … |
| maximal normal subgroup of | #14579755⋊C9, C9×#14579755, #37555873, … |
| maximal quotient of | C3×(C3×C97⋊C3)⋊C9, C3×(C97⋊C9)⋊C9, C3×#21463352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7857, 43);