Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D777 |
| unambiguous semidirect product | C3⋊(C7×D259) |
| unambiguous semidirect product | C7⋊(C7×D111) |
| unambiguous semidirect product | C37⋊(C7×D21) |
| Fitting, socle, Hall | C3×C72×C37 ⋊ C2 |
| derived | C3×C7×C37 ⋊ C2×C7 |
| Hall | C72×C37 ⋊ D3 |
| Hall | C3×C72 ⋊ D37 |
| Hall | C3×C37 ⋊ C7×D7 |
| Sylow | C72 ⋊ D111 |
| Sylow | C37 ⋊ C7×D21 |
| Sylow | C3 ⋊ C7×D259 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D777 |
| commutator, cosocle, hypocenter | C3×C7×C37 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C37 | C2 |
| LCS | G ▷ C3×C7×C37 | |
| UCS | C1 ◁ C7 | |
44 conjugacy classes of subgroups.
2730 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D21×D37, C7×D7×D111, D3×C7×D259, … |
| maximal normal subgroup of | C7×D21×D37, C7×D7×D111, D3×C7×D259, … |
| maximal quotient of | C7×Dic777, C2×C7×D777, C7×D2331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 92);