Finite Group DatabasebetaFinite Group Databasebeta| order | 7857 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C32×C97⋊C9 |
| derived, Sylow | C97 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | C97⋊C3 |
| commutator, hypocenter | C97 | C32×C9 |
| Frattini | C3 | C32×C97⋊C3 |
| Fitting, socle | C33×C97 | C3 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C33 | |
100 conjugacy classes of subgroups.
945 conjugacy classes — view the full character table.
| maximal subgroup of | C97⋊#6855, #37555790, #37555792, … |
| maximal normal subgroup of | C97⋊#6855, #37555790, #37555792, … |
| maximal quotient of | C3×C9×C97⋊C9, C3×C32⋊(C97⋊C9), C3×#21463351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7857, 39);